kaplansky classes and derived categories we put a monoidal model category structure on the category of chain complexes of quasi coherent sheaves over a quasi compact and semi separated scheme x the approach generalizes and simplifies the method used by the author in trans am math soc 356 8 3369 3390 2004 and trans am math soc 358 7 2855 2874 2006 to build monoidal model structures on the category of chain complexes of modules over a ring and chain complexes of sheaves over a ringed space indeed much of the paper is dedicated to showing that in any grothendieck category mathcal g any nice enough class of objects mathcal f induces a model structure on the category ch mathcal g of chain complexes the main technical requirement on mathcal f is the existence of a regular cardinal such that every object f in mathcal f satisfies the following property each generated subobject of f is contained in another generated subobject s for which s f s in mathcal f such a class mathcal f is called a kaplansky class kaplansky classes first appeared in enochs and lopez ramos rend sem mat univ padova 107 67 79 2002 in the context of modules over a ring r we study in detail the connection between kaplansky classes and model categories we also find simple conditions to put on mathcal f which will guarantee that our model structure is monoidal we will see that in several categories the class of flat objects form such kaplansky classes and hence induce monoidal model structures on the associated chain complex categories we will also see that in any grothendieck category mathcal g the class of all objects is a kaplansky class which induces the usual non monoidal injective model structure on ch mathcal g

spectra of modules abstract this manuscript solves the problem that the so called stable category mod of an artin algebra is in general not triangulated the method is to mimick topology and hence first form the spanier whitehead category stab mod and then construct a category spectra of spectra of modules which completes the compact part of stab mod under small coproducts spectra is then a triangulated substitute for mod the main results are that spectra is a compactly generated triangulated category which contains the compact part of stab mod as a full subcategory and even admits a precise description of its compact objects which only form a small set of isomorphism classes as an application it is proved that over an artin algebra the gorenstein projective modules form a pre covering class this was previously only known for rings satisfying strong homological conditions

the additivity of traces in triangulated categories abstract we explain a fundamental additivity theorem for euler characteristics and generalized trace maps in triangulated categories the proof depends on a refined axiomatization of symmetric monoidal categories with a compatible triangulation the refinement consists of several new axioms relating products and distinguished triangles the axioms hold in the examples and shed light on generalized homology and cohomology theories

almost free modules and mittag leffler conditions abstract drinfeld recently suggested to replace projective modules by the flat mittag leffler ones in the definition of an infinite dimensional vector bundle on a scheme x drinfeld 2006 8 two questions arise 1 what is the structure of the class d of all flat mittag leffler modules over a general ring 2 can flat mittag leffler modules be used to build a quillen model category structure on the category of all chain complexes of quasi coherent sheaves on x we answer 1 by showing that a module m is flat mittag leffler if and only if m is 1 projective in the sense of eklof and mekler 2002 10 we use this to characterize the rings such that d is closed under products and relate the classes of all mittag leffler strict mittag leffler and separable modules then we prove that the class d is not deconstructible for any non right perfect ring so unlike the classes of all projective and flat modules the class d does not admit the homotopy theory tools developed recently by hovey 2002 26 this gives a negative answer to 2

on the gravitational attraction of a right rectangular prism with density varying with depth following a cubic polynomial juan garcia abdeslem 2005 geophysics 66 1793 1804 the author presents an interesting note that a cubic polynomial would be more appropriate than a quadratic polynomial to simulate the density depth variation of sedimentary rocks when the depth is confined to 7 km the author demonstrates this by simulating the density depth data from the green canyon offshore louisiana as presented by li 2001

hearts of twin cotorsion pairs on extriangulated categories abstract in this article we study the heart of a cotorsion pairs on an exact category and a triangulated category in a unified method by means of the notion of an extriangulated category we prove that the heart is abelian and construct a cohomological functor to the heart if the extriangulated category has enough projectives this functor gives an equivalence between the heart and the category of coherent functors over the coheart modulo projectives we also show how an n cluster tilting subcategory of an extriangulated category gives rise to a family of cotorsion pairs with equivalent hearts

understanding imaging methods for potential field data several noniterative imaging methods for potential field data have been proposed that provide an estimate of the 3d magnetization density distribution within the subsurface or that produce images of quantities related or proportional to such distributions they have been derived in various ways using generalized linear inversion wiener filtering wavelet and depth from extreme points dexp transformations crosscorrelation and migration we demonstrated that the resulting images from each of these approaches are equivalent to an upward continuation of the data weighted by a possibly depth dependent function source distributions or related quantities imaged by all of these methods are smeared diffuse versions of the true distributions but owing to the stability of upward continuation resolution may be substantially increased by coupling derivative and upward continuation operators these imaging techniques appeared most effective in the case of isolated compact and depth limited sources beca

the flat model structure on given a cotorsion pair a b in an abelian category c with enough a objects and enough b objects we define two cotorsion pairs in the category ch c of unbounded chain complexes we see that these two cotorsion pairs are related in a nice way when a b is hereditary we then show that both of these induced cotorsion pairs are complete when a b is the flat cotorsion pair of r modules this proves the flat cover conjecture for possibly unbounded chain complexes and also gives us a new flat model category structure on ch r in the last section we use the theory of model categories to show that we can define ext n r m n using a flat resolution of m and a cotorsion coresolution of n

a multiple level set method for 3d inversion of magnetic data abstractwe have developed a multiple level set method for inverting magnetic data produced by weak induced magnetization only the method is designed to deal with a specific class of 3d magnetic inverse problems in which the magnetic susceptibility is known and the objective of the inversion is to find the boundary or geometric shape of the causative bodies we adopt the conceptual representation of the subsurface geologic structure by a set of magnetic bodies each having a uniform magnetic susceptibility embedded in a nonmagnetic background this representation enables us to reformulate the magnetic inverse problem into a domain inverse problem for those unknown domains defining the supports of the magnetic causative bodies because each body may take on a variety of shapes and we may not know the number of bodies a priori either we use multiple level set functions to parameterize these domains so that the domain inverse problem can be further reduced to an optimization problem of multiple level set f

model categories of quiver representations abstract gillespie s theorem gives a systematic way to construct model category structures on c m the category of chain complexes over an abelian category m we can view c m as the category of representations of the quiver 2 1 0 1 2 with the relations that two consecutive arrows compose to 0 this is a self injective quiver with relations and we generalise gillespie s theorem to other such quivers with relations there is a large family of these and following iyama and minamoto their representations can be viewed as generalised chain complexes our result gives a systematic way to construct model category structures on many categories this includes the category of n periodic chain complexes the category of n complexes where n 0 and the category of representations of the repetitive quiver z a n with mesh relations

covers envelopes and cotorsion theories in locally presentable abelian categories and contramodule categories we prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories extending the well established theory for module categories and grothendieck categories these results are then applied to the categories of contramodules over topological rings which provide examples and counterexamples

models for singularity categories abstract in this article we construct various models for singularity categories of modules over differential graded rings the main technique is the connection between abelian model structures cotorsion pairs and deconstructible classes and our constructions are based on more general results about localization and transfer of abelian model structures we indicate how recollements of triangulated categories can be obtained model categorically discussing in detail krause s recollement k ac inj r k inj r d r in the special case of curved mixed z graded complexes we show that one of our singular models is quillen equivalent to positselski s contraderived model for the homotopy category of matrix factorizations

model category structures arising from drinfeld vector bundles we present a general construction of model category structures on the category ch qco x of unbounded chain complexes of quasi coherent sheaves on a semi separated scheme x the construction is based on making compatible the filtrations of individual modules of sections at open affine subsets of x it does not require closure under direct limits as previous methods we apply it to describe the derived category mathbb d qco x via various model structures on ch qco x as particular instances we recover recent results on the flat model structure for quasi coherent sheaves our approach also includes the case of infinite dimensional vector bundles and of restricted flat mittag leffler quasi coherent sheaves as introduced by drinfeld finally we prove that the unrestricted case does not induce a model category structure as above in general

smashing localizations of rings of weak global dimension at most one abstract we show for a ring r of weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting in r if moreover r is commutative we prove that the compactly generated localizing subcategories correspond precisely to flat epimorphisms we also classify smashing localizations of the derived category of any valuation domain and provide an easy criterion for the telescope conjecture tc for any commutative ring of weak global dimension at most one as a consequence we show that the tc holds for any commutative von neumann regular ring r and it holds precisely for those prufer domains which are strongly discrete

parallei graph algorithms that are efficient on average the following three problems concerning random graphs can be solved in logn o 1 expected time using linearly many processors 1 finding the lexicographically first maximal independent set 2 coloring the vertices using a number of colors that is almost surely within twice the chromatic number and 3 finding a hamiltonian circuit

compact gravity inversion we present a new criterion for the inversion of gravity data the principle employed is to minimize the volume of the causative body which is equivalent to maximizing its compactness the anomalous density distribution is obtained using an iterative technique which is numerically stable and rapidly convergent the principle can also be adapted to include modeling of gravity anomalies by single density sources the advantage of this approach is that desirable geologic characteristics are automatically incorporated into the model with a minimum of subjective judgments on the part of the interpreter the treatment of noise in the data fits naturally into the formulation of the inversion procedure the method is illustrated by the inversion of noise free and noisy data generated from a two dimensional model consisting of a regular array of identical rectangular blocks whose densities can be individually specified in every case the algorithm successfully recovers the correct density distribution from the dat

covers and envelopes in grothendieck categories flat covers of complexes with applications abstract in the general setting of grothendieck categories with enough projectives we prove theorems that make possible to restrict the study of the problem of the existence of f covers and envelopes to the study of some properties of the class f we then prove the existence of flat covers and cotorsion envelopes of complexes giving some examples this generalizes the earlier work j algebra201 1998 86 102 and finishes the problem of the existence of flat covers of complexes

complexity and varieties for infinite groups i this two part paper generalizes the usual notion of complexity and varieties for modules over the group algebra of a finite group to a large class of infinite groups the context is modules of typefp for groups in kropholler s classlhf one of the main results is that the category of such modules is generated in a suitable sense by modules induced from finite elementary abelian subgroups this implies that an element of complete cohomology of such a module is nilpotent if and only if its restriction to every finite elementary abelian subgroup is nilpotent it also implies that the complexity of a module of typefp is finite and that the variety is supported on some finite collection of finite elementary abelian subgroups an example is given which shows that the complexity does not determine the rate of growth of the number of generators in a projective resolution in the way it does for finite groups

three dimensional gravity inversion using graph theory to delineate the skeleton of homogeneous sources abstractwe developed a new strategy based on graph theory concepts to invert gravity data using an ensemble of simple point masses our method consisted of a genetic algorithm with elitism to generate a set of possible solutions each estimate was associated to a graph to solve the minimum spanning tree mst problem to produce unique and stable estimates we restricted the position of the point masses by minimizing the statistical variance of the distances of an mst jointly with the data misfit function during the iterations of the genetic algorithm hence the 3d spatial distribution of the point masses identified the skeleton of homogeneous gravity sources in addition our method also gave an estimation of the anomalous mass of the source so together with the anomalous mass the skeleton could aid other 3d methods with promising geometric a priori parameters several tests with different values of regularizing parameter were made to bespeak this new regularizing strategy the inversion results ap

relative homological algebra in the category of quasi coherent sheaves abstract in this paper we prove the existence of a flat cover and of a cotorsion envelope for any quasi coherent sheaf over a scheme x o x indeed we prove something more general we define what it is understood by the category of quasi coherent r modules where r is a representation by rings of a quiver q and we prove the existence of a flat cover and a cotorsion envelope for quasi coherent r modules then we use the fact that the category of quasi coherent sheaves on x o x is equivalent to the category of quasi coherent r modules for some q and r to get our result

a distributed algorithm for finding hamiltonian cycles in random graphs in o logn time abstract it is known for some time that a random graph g n p contains w h p a hamiltonian cycle if p is larger than the critical value p c r i t log n log log n n n the determination of a concrete hamiltonian cycle for g n p is a nontrivial task even when p is much larger than p c r i t in this paper we consider random graphs g n p with p in 1 n where hides poly logarithmic factors in n for this range of p we present a distributed algorithm a hc that finds w h p a hamiltonian cycle in o log n rounds the algorithm works in the synchronous model and uses messages of size o log n and o log n memory per node

fourier forward modeling of vector and tensor gravity fields due to prismatic bodies with variable density contrast abstractprismatic bodies with variable density contrasts are very useful in modeling and inversion of gravity anomalies for sedimentary basins in which some simple mathematical functions offer better approximations for the density depth relationship of the basin fill than a constant density model we have explored fourier domain modeling of vector and tensor gravity anomalies due to 2d and 3d prismatic bodies following a wide class of variable density functions we placed the emphasis on general polynomial models because they provided a flexible way to approximate arbitrary density functions the recently proposed gauss fast fourier transform method was applied to improve the accuracy of inverse fourier transform the numerical performance of the presented method was examined by comparing with space domain analytical seminumerical or completely numerical solutions singularity and numerical stability of the algorithm were also analyzed with ranges of numerical stability for polynomial density models of

3 d inversion of gravity data we present two methods for inverting surface gravity data to recover a 3 d distribution of density contrast in the first method we transform the gravity data into pseudomagnetic data via poisson s relation and carry out the inversion using a 3 d magnetic inversion algorithm in the second we invert the gravity data directly to recover a minimum structure model in both approaches the earth is modeled by using a large number of rectangular cells of constant density and the final density distribution is obtained by minimizing a model objective function subject to fitting the observed data the model objective function has the flexibility to incorporate prior information and thus the constructed model not only fits the data but also agrees with additional geophysical and geological constraints we apply a depth weighting in the objective function to counteract the natural decay of the kernels so that the inversion yields depth information applications of the algorithms to synthetic and field data produce density models representative of true structures our results have shown that the inversion of gravity data with a properly designed objective function can yield geologically meaningful information

on the exactness of products in the localization of ab 4 grothendieck categories abstract let c be an ab 4 grothendieck category that is products are exact in c given a hereditary torsion class t c we study the exactness of products in the gabriel localization c t of c we show that under suitable assumptions on c the k 1 th derived functor of the product vanishes provided the gabriel dimension of c t is smaller than k as a consequence we deduce that under suitable hypotheses the derived category d c t is left complete

quillen equivalences for stable categories abstract for an abelian category a we investigate when the stable categories gpro j a and gin j a are triangulated equivalent to this end we realize these stable categories as homotopy categories of certain non trivial model categories and give conditions on a that ensure the existence of a quillen equivalence between the model categories in question we also study when such a quillen equivalence transfers from a to the category of chain complexes in a

higher comparison maps for the spectrum of a tensor triangulated category abstract for each object in a tensor triangulated category we construct a natural continuous map from the object s support a closed subset of the category s triangular spectrum to the zariski spectrum of a certain commutative ring of endomorphisms when applied to the unit object this recovers a construction of p balmer these maps provide an iterative approach for understanding the spectrum of a tensor triangulated category by starting with the comparison map for the unit object and iteratively analyzing the fibers of this map via higher comparison maps we illustrate this approach for the stable homotopy category of finite spectra in fact the same underlying construction produces a whole collection of new comparison maps including maps associated to and defined on each closed subset of the triangular spectrum these latter maps provide an alternative strategy for analyzing the spectrum by iteratively building a filtration of closed subsets by pulling back filtrations of affine schemes

3d magnetic sparse inversion using an interior point method rock susceptibility measurements are sometimes taken on outcrop and borehole rocks and provide valuable information for constraining magnetic data inversion we present two approaches for 3d magnetic sparse inversion that effectively take advantage of the rock susceptibility information both approaches minimize a total objective function subject to bound constraints using an interior point method the first approach directly minimizes an l1 norm of the susceptibility model by keeping the bounds positive in which case the objective function is differentiable in the feasible region the second approach minimizes a more generalized lp like norm 0 p 1 of the susceptibility model by approximating the lp like norm inversion as an iteratively reweighed least squares problem moreover this approach allows the model values to be either positive or negative we also demonstrate the equivalence of the proposed approaches and the binary inversion the recovered models of both approaches are characterized by

2 d gravity modeling with analytically defined geometry and quadratic polynomial density functions new methods for 2 d modeling of gravity anomaly data are developed following an approach that uses both analytic and numerical methods of integration the forward model solution developed here is suitable to calculate the gravity effect caused by a 2 d source body bounded either laterally or vertically by continuous functions in our models the density contrast is defined by a second order polynomial function of depth and distance along the profile we present several examples to show that our models are capable of accommodating a broad variety of geologic structures

flat covers in abelian and in non abelian categories abstract a general existence theorem for flat covers in e g quasi abelian locally finitely presented categories is obtained from an additive ramsey type theorem in the abelian case it is shown that flat covers always exist applications to categories of separated presheaves or sheaves localizations of bousfield type torsion free classes of finite type and categories of filtered objects or complexes are given

homotopy equivalences induced by balanced pairs abstract we introduce the notion of balanced pair of additive subcategories in an abelian category we give sufficient conditions under which a balanced pair of subcategories gives rise to a triangle equivalence between two homotopy categories of complexes as an application we prove that for a left gorenstein ring there exists a triangle equivalence between the homotopy category of its gorenstein projective modules and the homotopy category of its gorenstein injective modules which restricts to a triangle equivalence between the homotopy category of projective modules and the homotopy category of injective modules in the case of commutative gorenstein rings we prove that up to a natural isomorphism our equivalence extends iyengar krause s equivalence

abstract representation theory of dynkin quivers of type a abstract we study the representation theory of dynkin quivers of type a in abstract stable homotopy theories including those associated to fields rings schemes differential graded algebras and ring spectra reflection functors partial coxeter functors and serre functors are defined in this generality and these equivalences are shown to be induced by universal tilting modules certain explicitly constructed spectral bimodules in fact these universal tilting modules are spectral refinements of classical tilting complexes as a consequence we obtain split epimorphisms from the spectral picard groupoid to derived picard groupoids over arbitrary fields these results are consequences of a more general calculus of spectral bimodules and admissible morphisms of stable derivators as further applications of this calculus we obtain examples of universal tilting modules which are new even in the context of representations over a field this includes yoneda bimodules on mesh categories which encode all the other universal tilting modules and which lead to a spectral serre duality result finally using abstract representation theory of linearly oriented a n quivers we construct canonical higher triangulations in stable derivators and hence a posteriori in stable model categories and stable categories

distributed algorithms for random graphs in this article we study statistical properties of a commonly used network model an erd s renyi random graph g n p we are interested in the performance of distributed algorithms on large networks which might be represented by g n p we concentrate on classical problems from the field of distributed algorithms such as finding a maximal independent set a vertex colouring an approximation of a minimum dominating set a maximal matching an edge colouring and an approximation of a maximum matching we propose new algorithms which with probability close to one as n construct anticipated structures in g n p in a low number of rounds moreover in some cases we modify known algorithms to obtain better efficiency on g n p

model category structures on chain complexes of sheaves in this paper we try to determine when the derived category of an abelian category is the homotopy category of a model structure on the category of chain complexes we prove that this is always the case when the abelian category is a grothendieck category as has also been done by morel but this model structure is not very useful for dening derived tensor products we therefore consider another method for constructing a model structure and apply it to the category of sheaves on a well behaved ringed space the resulting flat model structure is compatible with the tensor product and all homomorphisms of ringed spaces

derived equivalences induced by big cotilting modules abstract we prove that given a grothendieck category g with a tilting object of finite projective dimension the induced triangle equivalence sends an injective cogenerator of g to a big cotilting module moreover every big cotilting module can be constructed like that in an essentially unique way we also prove that the triangle equivalence is at the base of an equivalence of derivators which in turn is induced by a quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes

three dimensional fourier gravity inversion with arbitrary density contrast the use of variable density contrasts in gravity inversion has gained increasing importance in recent years due to the necessity of constructing more realistic models of geophysical structures such as sedimentary basins linear quadratic and exponential variations either in the space or in the frequency domain are the basis of several methods see among others the papers by granser 1987 chai and hinze 1988 reamer and ferguson 1989 and rao et al 1990 guspi 1990 used polynomial density depth functions for inverting gravity anomalies into 2 d polygons in the space domain

high precision fourier forward modeling of potential fields we analyzed the numerical forward methods in the fourier domain for potential fields existing fourier domain forward methods applied the standard fast fourier transform fft algorithm to inverse transform a conjugate symmetrical spectrum into a real field it had significant speed advantages over space domain forward methods but suffered from problems including aliasing imposed periodicity and edge effect usually grid expansion was needed to reduce these errors which was equivalent to the numerical evaluation of the oscillatory fourier integral using the trapezoidal rule with smaller steps we tested a high precision fourier domain forward method based on a combined use of shift sampling technique and gaussian quadrature theory the trapezoidal rule applied by the standard fft algorithm to evaluate the continuous fourier transform was modified by introducing a shift parameter by choosing optimum values of as gaussian quadrature nodes we developed a gauss fft method for fourier forward modeling of potential fields no grid expansion was needed the sources can be set near the boundary of the fields or even go beyond the boundary the gauss fft method converged to the space domain solution much faster than the standard fft method with grid expansion forward modeling results almost identical to space domain ones can be obtained in less time numerical examples of both simple and complex 2d and 3d source forward modeling revealed the reliability and adaptability of the method

cross gradients joint 3d inversion with applications to gravity and magnetic data we extend the cross gradient methodology for joint inversion to three dimensional environments and introduce a solution procedure based on a statistical formulation and equality constraints for structural similarity resemblance we apply the proposed solution to the joint 3d inversion of gravity and magnetic data and gauge the advantages of this new formulation on test and field data experiments combining singular value decomposition svd and other conventional regularizing constraints we determine 3d distributions of the density and magnetization with enhanced structural similarity the algorithm reduces some misleading features of the models which are introduced commonly by conventional separate inversions of gravity and magnetic data and facilitates an integrated interpretation of the models

cartesian modules over representations of small categories we introduce the new concept of cartesian module over a pseudofunctor r from a small category to the category of small preadditive categories already the case when r is a strict functor taking values in the category of commutative rings is sucient

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

gorenstein complexes and recollements from cotorsion pairs we describe a general correspondence between injective resp projective recollements of triangulated categories and injective resp projective cotorsion pairs this provides a model category description of these recollement situations our applications focus on displaying several recollements that glue together various full subcategories of k r the homotopy category of chain complexes of modules over a general ring r when r is left noetherian these recollements involve complexes built from the gorenstein injective modules when r is a left coherent ring for which all flat modules have finite projective dimension we obtain the duals these results extend to a general ring r by replacing the gorenstein modules with the gorenstein ac modules introduced in 9 we also see that in any abelian category with enough injectives the gorenstein injective objects enjoy a maximality property in that they contain every other class making up the right half of an injective cotorsion pair

practical applications of uniqueness theorems in gravimetry part ii pragmatic incorporation of concrete geologic information we illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute we also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth independent density distributions the two part guideline is 1 to introduce a priori information favoring uniqueness either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous simply connected polygons or polyhedra with known density displaying no fancy shapes and no curling apophyses at their borders and 2 to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data following the guideline we apply different methods to gravity data using interp

conjugate complex variables method for the computation of gravity anomalies using conjugate complex variables a generalized method is presented to derive formulas to calculate first and higher order derivatives of the gravity potential due to selected mass models double integrals in the computation of gravity gradient anomalies are transformed into complex contour integrals analytical expressions for higher order derivatives of the gravitational potential in arbitrary directions due to two dimensional 2 d polygonal mass models are derived the method is extended to 2 d polygonal bodies whose density contrasts vary with depth and horizontal distance and can be generalized to deal with 2 d bodies of any shape the vertical gravity field and its first derivatives due to a homogeneous radially symmetric body are also computed using conjugate complex variables derivation of gravity and gravity gradient formulas generally is greatly simplified by the use of complex variables

on projectivity in locally presentable categories abstract we show that some fundamental results about projectivity classes weakly coreflective subcategories and cotorsion theories can be generalized from r modules to arbitrary locally presentable categories

cartan eilenberg complexes and resolutions abstract we study cartan eilenberg projective injective and flat complexes and show how they can be used to get cartan eilenberg resolutions we argue that every complex has a cartan eilenberg injective envelope then we show that a complex is a cartan eilenberg flat complex if and only if it is the direct limit of finitely generated cartan eilenberg projective complexes

exact model structures and recollements abstract we show how to obtain recollements of triangulated categories using the theory of exact model structures from 13 after noting how the theory relates to well known notions in the simplest case of frobenius categories we apply these ideas to recollements of homotopy categories of chain complexes in short we give model categorical explanations for the classical verdier localization recollement as well as several recollement situations due to neeman and murfet

inversion modeling of gravity with prismatic mass bodies a combined method for forward and inverse modeling of gravity data is presented based on the fourier transform of poisson s equation the forward modeling is suitable for observation points above within and below causative masses with any prescribed density distribution the inversion is linearized in the spatial domain by superimposing numerous prismatic bodies each having constant but different density and fixed geometry our inversion algorithm adopts a sampling window to reduce memory storage and computations testing with synthetic and field data demonstrates that a successful inversion can be obtained from crudely estimated a priori density distributions and uncertainties lateral variations in density are well resolved but depth resolution often requires better constrained a priori information under various a priori conditions our modeling indicates that sediment density tends to vary exponentially with depth in the san jacinto basin southern california

a versatile solution for the gravity anomaly of 3d prism meshed bodies with depth dependent density contrast abstractwe have developed a generalized solution for computing the gravity anomalies of 3d irregular mass bodies with complicated density contrast variation the 3d irregular shaped bodies can be approximated flexibly by a collection of finite juxtaposed right rectangular prisms the complicated density contrast variation of each prism can be well represented by a depth dependent polynomial function a novel analytic solution of gravity anomalies due to a right rectangular prism with an arbitrary order of polynomial density contrast function of depth is then derived the solution is singularity free in the upper half space over the prism and its singularity in the lower half space containing the prism is resolved by assigning their limit values to the singular terms the numerical stability of the solution is also evaluated through numerical tests hence the solution can be used to compute the gravity anomalies of 3d irregular bodies with variable density contrasts without singularities when computation

a nonparametric boundary detection technique applied to 3d inverted surveys of the kevitsa ni cu pge deposit abstractgeophysical inversion can produce 3d models of the subsurface s physical properties the smoothness of property variations in these models makes it challenging to automatically find boundaries of homogeneous regions where these boundaries may have implications for petrophysical transition and are significant for geologic interpretation we have developed a new boundary detection technique that nonparametrically identifies and subtracts homogeneous regions from the 3d model leaving exposed edges the method is based on kernel density estimation of local property variations in which the number of modes in the kernel density estimates i e the local mode cardinality mc is used to identify edge voxels within the model two edge detection operators were developed one using local values exclusively and the other incorporating the spatial distribution of local values into the local mc which is more sensitive to local variations to assist in the geologic interpretation continuous boundary surf

3d vector gravity potential and line integrals for the gravity anomaly of a rectangular prism with 3d variable density contrast three dimensional rectangular prisms are building blocks for calculating gravity anomalies from irregular 3d mass bodies with spatially variable density contrasts a 3d vector gravity potential is defined for a 3d rectangular prism with density contrast varying in depth and horizontally the vertical component of the gravity anomaly equals the flux of the 3d vector gravity potential through the enclosed surface of the prism thus the 3d integral for the gravity anomaly is reduced to a 2d surface integral in turn a 2d vector gravity potential is defined the vertical component of the gravity anomaly equals the net circulation of the 2d vector gravity potential along the enclosed contour bounding the surfaces of the prism the 3d integral for the gravity anomaly is reduced to 1d line integrals further analytical or numerical solutions can then be obtained from the line integrals depending on the forms of the density contrast functions if an analytical solution cannot be obtained the line integral method is semianalytical requiring numerical quadratures to be carried out at the final stages singularity and discontinuity exist in the algorithm and the method of exclusive infinitesimal sphere or circle is effective to remove them then the vector potential line integral method can calculate the gravity anomaly resulting from a rectangular prism with density contrast varying simply in one direction and sophisticatedly in three directions the advantage of the method is that the constraint to the form of the density contrast is greatly reduced and the numerical calculation for the gravity anomaly is fast

some adjoints in homotopy categories let r be a ring in a previous paper 11 we found a new description for the category k r proj it is equivalent to the verdier quotient k r flat s for some suitable s c k r flat in this article we show that the quotient map from k r flat to k r flat s always has a right adjoint this gives a new fully faithful embedding of k r proj into k r flat its virtue is that it generalizes to nonaffine schemes

elementary varieties and existence of flat covers abstract it is shown that flat covers exist in a wide class of additive categories we call them elementary which behave similar to locally finitely presented grothendieck categories elementary categories have enough finitely presented objects but they need not be locally finitely presented this is related to the existence of pure monomorphisms which are not kernels and the non exactness of direct limits for a module category mod r every class of r modules containing r cogenerates an elementary full subcategory

flat covers of complexes abstract in this article we define and study flat complexes over any ring also we prove that any complex over a commutative noetherian ring with finite krull dimension has a flat cover and a dg flat cover

2d vector gravity potential and line integrals for the gravity anomaly caused by a 2d mass of depth dependent density contrast using line integrals lis used to calculate the gravity anomaly caused by a 2d mass of complicated geometry and spatially variable density contrast is a computationally efficientalgorithm thatreducesthecalculationfromtwodimensions to one dimension this work has developed a mechanism for defining lis systematically for different types of density functions two dimensional vector gravity potential is defined as a vector the net circulation of which along the closedcontourboundinga2dmass equalsthegravityanomaly caused by the 2d mass two representative types of lis aredefined anliwithanarctangentkernelforanydepth dependent density contrast function which has been studied historically and an li with a simple algebraic kernel for any integrabledensity contrastfunction thepresentworkoffers 1avectorial basedderivationofformulasthatdonotsuffer from the arbitrary sign conventions found in some historical approaches and2asimplealgebraickernelinlineintegrals as an alternative to the historical arctangent kernel with the possibilityofextensiontomoregeneralcases theconceptof 2dvectorgravitypotentialprovidesausefultoolfordefining lis systematically for any mass density function helping us understand how dimensions can be reduced in a calculating gravity anomaly especially when the density contrast varies with space lis have been tested in case studies the maximumdifferencesincalculatedgravityanomaliesbydifferent lis for the case studies were between 5 9310

the derived category of quasi coherent sheaves and axiomatic stable homotopy we prove in this paper that for a quasi compact and semi separated nonnecessarily noetherian scheme x the derived category of quasi coherent sheaves over x is a stable homotopy category in the sense of hovey palmieri and strickland answering a question posed by strickland moreover we show that it is unital and algebraic we also prove that for a noetherian semi separated formal scheme its derived category of sheaves of modules with quasi coherent torsion homologies is a stable homotopy category it is algebraic but if the formal scheme is not a usual scheme it is not unital therefore its abstract nature differs essentially from that of the derived category which is equivalent to in the case of a usual scheme

gravity inversion of an interface above which the density contrast varies exponentially with depth mapping of an interface above which the density contrast varies exponentially with depth as is common at the basement surface of sedimentary basins is efficiently achieved by a theoretically precise gravity method which can be applied to either profile data or twodimensional data the contrast in mass above the interface is modeled by an array of vertical rectangular prisms with density contrasts varying exponentially with depth gravity anomalies due to the prisms are calculated in the wavenumber domain and then converted to the space domain the precision of the inverse numerical fourier transform in this procedure is significantly increased by a shift sampling technique based on the discrete fourier deviation equation depth to the interface is determined by iterative adjustment of the vertical extent of the prisms in accordance with observed gravity anomaly data the basement surface of the los angeles basin california calculated by this method closely duplicates the published configuration based

proper classes and gorensteinness in extriangulated categories abstract extriangulated categories were introduced by nakaoka and palu as a simultaneous generalization of exact categories and triangulated categories a notion of proper class in an extriangulated category is defined in this paper let c be an extriangulated category and a proper class in c we prove that c admits a new extriangulated structure this construction gives extriangulated categories which are neither exact categories nor triangulated categories moreover we introduce and study gorenstein projective objects in c and demonstrate that gorenstein projective objects share some basic properties with gorenstein projective objects in module categories or in triangulated categories in particular we refine a result of asadollahi and salarian 2004 1 as an application the admissible model structure on extriangulated categories is obtained

gravity and magnetic inversion with minimization of a specific functional the nonuniqueness of gravity or magnetic data inversion is well known in order to remove ambiguity some authors have sought solutions minimizing a functional describing geometrical or physical properties last and kubik 1983 in particular developed a method explaining the observed anomaly by structures of minimum volume in this method the domain where anomalous sources are searched is divided into elementary prisms of a constant density or susceptibility contrast each elementary contrast is allowed to vary individually thus a contrast distribution is computed the search for this kind of solution leads in general to geologically more appropriate bodies but exceptions do occur in this paper the technique is broadened to include the search for solutions minimizing the moment of inertia with respect to the center of gravity or with respect to a given dip line passing through it the resulting structures are both deeper and more compact precisely as is required in specific cases theoretical and

structural inversion of gravity data using linear programming structural inversion of gravity data deriving robust images of the subsurface by delineating lithotype boundaries using density anomalies is an important goal in a range of exploration settings e g ore bodies salt flanks application of conventional inversion techniques in such cases using l2 norms and regularization produces smooth results and is thus suboptimal we investigate an l1 norm based approach which yields structural images without the need for explicit regularization the density distribution of the subsurface is modeled with a uniform grid of cells the density of each cell is inverted by minimizing the l1 norm of the data misfit using linear programming lp while satisfying a priori density constraints the estimate of the noise level in a given data set is used to qualitatively determine an appropriate parameterization the 2 5d and 3d synthetic tests adequately reconstruct the structure of the test models the quality of the inversion depends upon a good prior estimation of

the flat model structure on complexes of sheaves let ch o be the category of chain complexes of 0 modules on a topological space t where o is a sheaf of rings on t we put a quillen model structure on this category in which the cofibrant objects are built out of flat modules more precisely these are the dg flat complexes dually the fibrant objects will be called dg cotorsion complexes we show that this model structure is monoidal solving the previous problem of not having any monoidal model structure on ch o as a corollary we have a general framework for doing homological algebra in the category sh 0 of 0 modules i e we have a natural way to define the functors ext and tor in sh o

triangulated equivalence between a homotopy category and a triangulated quotient category abstract given two complete hereditary cotorsion pairs q r and q r in a bicomplete abelian category g such that q q and q r q r becker showed that there exists a hereditary abelian model structure m q w r on g where w is a thick subcategory of g we prove that the homotopy category ho m of m is triangulated equivalent to the triangulated quotient category d b g q r k b q r where d b g q r is the subcategory of d b g consisting of all homology bounded complexes with both finite q dimension and r dimension and k b q r is the bounded homotopy category of q r core objects applications are given in the category of modules it is shown that the homotopy category of the gorenstein flat resp ding projective and gorenstein ac projective model structure on the category of modules established by gillespie and his coauthors can be realized as a certain triangulated quotient category

brief paper quantized consensus in hamiltonian graphs the main contribution of this paper is an algorithm to solve an extended version of the quantized consensus problem over networks represented by hamiltonian graphs i e graphs containing a hamiltonian cycle which we assume to be known in advance given a network of agents we assume that a certain number of tokens should be assigned to the agents so that the total number of tokens weighted by their sizes is the same for all the agents the algorithm is proved to converge almost surely to a finite set containing the optimal solution a worst case study of the expected convergence time is carried out thus proving the efficiency of the algorithm with respect to other solutions recently presented in the literature moreover the algorithm has a decentralized stop criterion once the convergence set is reached

picard groups grothendieck rings and burnside rings of categories abstract we discuss the picard group the grothendieck ring and the burnside ring of a symmetric monoidal category and we consider examples from algebra homological algebra topology and algebraic geometry

gorenstein homological algebra and universal coefficient theorems we study criteria for a ring or more generally for a small category to be gorenstein and for a module over it to be of finite projective dimension the goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones among the universal coefficient theorems covered by our methods we find besides all the classic examples several exotic examples arising from the kk theory of c algebras and also neeman s brown adams representability theorem for compactly generated categories

on exact categories and applications to triangulated adjoints and model structures abstract we show that quillen s small object argument works for exact categories under very mild conditions this has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model structures in particular the interplay of different exact structures on the category of complexes of quasi coherent sheaves leads to a streamlined and generalized version of recent results obtained by estrada gillespie guil asensio hovey jorgensen neeman murfet prest trlifaj and possibly others

cotorsion pairs model category structures and representation theory we make a general study of quillen model structures on abelian categories we show that they are closely related to cotorsion pairs which were introduced by salce sal79 and have been much studied recently by enochs and coauthors ej00 this gives a method of constructing model structures on abelian categories which we illustrate by building two model structures on the category of modules over a possibly noncommutative gorenstein ring the homotopy category of these model structures is a generalization of the stable module category much used in modular representation theory this stable module category has also been studied by benson ben97

ideal approximation theory abstract let a e be an exact category and f ext a subfunctor a morphism in a is an f phantom if the pullback of an e conflation along is a conflation in f if the exact category a e has enough injective objects and projective morphisms it is proved that an ideal i of a is special precovering if and only if there is a subfunctor f ext with enough injective morphisms such that i is the ideal of f phantom morphisms a crucial step in the proof is a generalization of salce s lemma for ideal cotorsion pairs if i is a special precovering ideal then the ideal cotorsion pair i i generated by i in a e is complete this theorem is used to verify 1 that the ideal cotorsion pair cogenerated by the pure injective modules of r mod is complete 2 that the ideal cotorsion pair cogenerated by the contractible complexes in the category of complexes ch r mod is complete and using auslander and reiten s theory of almost split sequences 3 that the ideal cotorsion pair cogenerated by the jacobson radical jac mod of the category mod of finitely generated representations of an artin algebra is complete

tilting theory via stable homotopy theory we show that certain tilting results for quivers are formal consequences of stability and as such are part of a formal calculus available in any abstract stable homotopy theory thus these results are for example valid over arbitrary ground rings for quasi coherent modules on schemes in the differential graded context in stable homotopy theory and also in the equivariant motivic or parametrized variant thereof in further work we will continue developing this calculus and obtain additional abstract tilting results here we also deduce an additional characterization of stability based on goodwillie s strongly co cartesian n cubes as applications we construct abstract auslander reiten translations and abstract serre functors for the trivalent source and verify the relative fractionally calabi yau property this is used to offer a new perspective on may s axioms for monoidal triangulated categories