mild solutions to the time fractional navier stokes equations in r n abstract this paper addresses the existence and uniqueness of mild solutions to the navier stokes equations with time fractional differential operator of order 0 1 several interesting properties about the solution are also highlighted like regularity and decay rate in lebesgue spaces which will depend on the fractional exponent moreover it is shown that the l p exponent range which the solution belongs to is different from the range for the solution of the classical problem with 1

a utd triple diffraction coefficient for straight wedges in arbitrary configuration a new utd solution is presented for the description of the ray triply diffracted by straight wedges in arbitrary configuration illuminated by a spherical wavefront field the proposed utd coefficient permits to uniformly describe the field at any aspect in particular including the case of overlapping transition regions where the subsequent application of utd single wedge diffraction coefficient fails the triple diffracted ray field is expressed in an analytical form providing physical insight into the triple diffraction mechanism and a new effective engineering tool within the utd framework as required in a modern ray based code

a novel characteristic of solution operator for the fractional abstract cauchy problem abstract motivated by an equality of the mittag leffler function proved recently by the authors this paper develops an operator theory for the fractional abstract cauchy problem facp with order 0 1 the notion of fractional semigroup is introduced it is proved that a family of bounded linear operator is a solution operator for facp if and only if it is a fractional semigroup moreover the well posedness of the problem facp is also discussed it is shown that the problem facp is well posed if and only if its coefficient operator generates a fractional semigroup

on some fractional evolution equations abstract in this paper the solutions of some evolution equations with fractional orders in a banach space are considered conditions are given which ensure the existence of a resolvent operator for an evolution equation in a banach space

valuations and multiplier ideals this article is the third of a series of work on a new approach to the study of singularities of various objects in a local two dimensional setting our focus in the present paper is on multiplier ideals and singularity exponents in the discussion below we fix an equicharacteristic zero two dimensional regular local ring r m with algebraically closed residue field an important example is the ring r do o holomorphic germs at the origin in c2 in fj1 we introduced the space v consisting of all r u 00 valued valuations on r centered at m and normalized by m 1 this space is naturally a tree it is a union of uncountably many real segments patched together in such a way that v remains homotopic to a point it is also an r tree in the classical sense for a natural metric we hence call v the valuative tree it encodes in a natural way all possible blowups of r centered at m and therefore gives a way of measuring quite precisely singularities of different kinds of objects the points in v that are not ends form the subtree vqm of quasimonomial valuations these valuations which can alternatively be characterized as abhyankar valuations of rank 1 or as

valuative analysis of planar plurisubharmonic functions we show that valuations on the ring r of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions giving rise to generalized lelong numbers in the sense of demailly any plurisubharmonic function thus defines a real valued function on the set mathcal v of valuations on r and by way of a natural laplace operator defined in terms of the tree structure on mathcal v a positive measure on mathcal v this measure contains a great deal of information on the singularity at the origin under mild regularity assumptions it yields an exact formula for the mixed monge ampere mass of two plurisubharmonic functions as a consequence any generalized lelong number can be interpreted as an average of valuations using our machinery we also show that the singularity of any positive closed 1 1 current t can be attenuated in the following sense there exists a finite composition of blowups such that the pull back of t decomposes into two parts the first associated to a divisor with normal crossing support the second having small lelong numbers

a numerical criterion for very ample line bundles let x be a projective algebraic manifold of dimension n and let l be an ample line bundle over x we give a numerical criterion ensuring that the adjoint bundle kx l is very ample the sufficient conditions are expressed in terms of lower bounds for the intersection numbers l y over subvarieties y of x in the case of surfaces our criterion gives universal bounds and is only slightly weaker than i reider s criterion when dimx 3 and codimy 2 the lower bounds for l y involve a numerical constant which depends on the geometry of x by means of an iteration process it is finally shown that 2kx ml is very ample form 12n our approach is mostly analytic and based on a combination of hormander s l estimates for the operator lelong number theory and the aubin calabi yau theorem

a novel utd type diffraction coefficient for a straight edge in a curved screen a novel uniform theory of diffraction utd type diffraction coefficient for a straight edge in a cylindrically curved screen valid for both convex and concave side wave incidence is obtained via uniform asymptotic theory of diffraction uat formulations the proposed curved screen utd type coefficient csutd allows uniform description of the fields at all aspect angles including the grazing incidence case where utd coefficient based predictions deviate sharply from available measurements when it is applied to the problem of monostatic radar cross section rcs of cylindrically curved plate

diffraction of an obliquely incident high frequency wave by a cylindrically curved sheet in the application of the geometrical theory of diffraction gtd to practical problems a main role is played by the diffraction coefficients of different kinds nevertheless the explicit expressions of the diffraction coefficients associated with edges on certain curved sheets are known only in the case of normal incidence the canonical problems from which these coefficients are derived can always be reduced to scalar diffraction problems involving two space variables in which either the electric or the magnetic field is parallel to the edge nevertheless when the incident ray is not normal to the edge at the diffraction point the related canonical problems inevitably involve three space coordinates and at least two dependent functions the complexity inherent in such problems caused a lack of knowledge about the diffraction coefficients connected with the edges on curved sheets in the case of oblique incidence the case of oblique incidence on a perfectly conducting cylindrical sheet is considered and some explicit expressions for the matrix diffraction coefficients are derived these matrices connect the diffracted far fields of different kinds to the incident electric and magnetic field components parallel to the edge at the diffraction point the expressions are rather simple and involve the coefficients related to the case of normal incidence in which k is replaced by k sin theta 0 k and theta 0 are the wavenumber and the incidence angle respectively the effect of the incidence angle in the attenuation constants associated with the creeping waves are dependent upon theta 0 only via the curvature radius of the geodesic lines

a proof of demailly s strong openness conjecture in this article we solve the strong openness conjecture on the multiplier ideal sheaf associated to any plurisubharmonic function which was posed by demailly the multiplier ideal sheaf associated to a plurisubharmonic function which is an invariant of the singularities of the psh function plays an important role in several complex variables and complex geometry various properties about the multiplier ideal sheaves associated to plurisubharmonic functions have been discussed e g see 25 7 30 31 demailly s strong openness conjecture means that the strong openness property about the multiplier ideal sheaf holds in the present article we establish such a useful strong openness property on the multiplier ideal sheaf associated to any plurisubharmonic function i e demailly s strong openness conjecture is true 1 1 organization of the paper the paper is organized as follows in the present section we recall the statement of the strong openness conjecture posed by demailly and present the main result of the present paper a solution of the strong openness conjecture in section 2 we recall or give some preliminary lemmas used in the proof of the main result in section 3 we give the proof of the strong openness conjecture and present some consequences by combining the conjecture with some well known results

conical kahler einstein metrics revisited in this paper we introduce the interpolation degeneration strategy to study kahler einstein metrics on a smooth fano manifold with cone singularities along a smooth divisor that is proportional to the anti canonical divisor by interpolation we show the angles in 0 2 that admit a conical kahler einstein metric form a connected interval and by degeneration we determine the boundary of the interval in some important cases as a first application we show that there exists a kahler einstein metric on mathbb p 2 with cone singularity along a smooth conic degree 2 curve if and only if the angle is in 2 2 when the angle is 2 3 this proves the existence of a sasaki einstein metric on the link of a three dimensional a2 singularity and thus answers a question posed by gauntlett martelli sparks yau as a second application we prove a version of donaldson s conjecture about conical kahler einstein metrics in the toric case using song wang s recent existence result of toric invariant conical kahler einstein metrics

harnack s inequality for a space time fractional diffusion equation and applications to an inverse source problem abstract in this paper we focus on a space time fractional diffusion equation with the generalized caputo s fractional derivative operator and a general space nonlocal operator with the fractional laplace operator as a special case a weak harnack s inequality has been established by using a special test function and some properties of the space nonlocal operator based on the weak harnack s inequality a strong maximum principle has been obtained which is an important characterization of fractional parabolic equations with these tools we establish a uniqueness result of an inverse source problem on the determination of the temporal component of the inhomogeneous term which seems to be the first theoretical result of the inverse problem for such a general fractional diffusion model

greatest lower bounds on ricci curvature for toric fano manifolds abstract in this short note based on the work of wang and zhu 2004 8 we determine the greatest lower bounds on ricci curvature for all toric fano manifolds

on the solution of fractional evolution equations this paper is devoted to the solution of the bi fractional differential equation for real 0 0 and 0 with the initial conditions here cd tu t x is the partial derivative coinciding with the caputo fractional derivative for 0 0 the laplace and fourier transforms are applied to solve the above problem in closed form the fundamental solution of these problems is established and its moments are calculated the special case 1 2 and 1 is presented and its application is given to obtain the dirac type decomposition for the ordinary diffusion equation

solution to a non archimedean monge ampere equation let x be a smooth projective berkovich space over a complete discrete valuation field k of residue characteristic zero and assume that x is defined over a function field admitting k as a completion let further m be a positive measure on x and l be an ample line bundle such that the mass of m is equal to the degree of l then we show the existence a continuous semipositive metric whose associated measure is equal to m in the sense of zhang and chambert loir this we do under a technical assumption on the support of m which is for instance fulfilled if the support is a finite set of divisorial points our method draws on analogues of the variational approach developed to solve complex monge ampere equations on compact kahler manifolds by berman guedj zeriahi and the first named author and of ko l odziej s continuity estimates it relies in a crucial way on the compactness properties of singular semipositive metrics as defined and studied in a companion article

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

a note on property of the mittag leffler function abstract recently the authors have found in some publications that the following property 0 1 of mittag leffler function is taken for granted and used to derive other properties 0 1 e a t s e a t e a s t s 0 where a is a real constant and 0 in this note it is proved that the above property is unavailable unless 1 or a 0 moreover a new equality on e a t is developed whose limit state as 1 is just the property 0 1