bluuebunny/crossref_metadata_2025_split huggingface dataset:
Derived equivalences and stable equivalences of Morita type, I
Authors: Hu Wei , Xi Changchang 
Published: July 2016

AbstractFor self-injective algebras, Rickard proved that each derived equivalence induces a stable equivalence of Morita type. For general algebras, it is unknown when a derived equivalence implies a stable equivalence of Morita type. In this article, we first show that each derived equivalenceFbetween the derived categories of Artin algebrasAandBarises naturally as a functorbetween their stable module categories, which can be used to compare certain homological dimensions ofAwith that ofB. We then give a sufficient condition for the functorto be an equivalence. Moreover, if we work with finite-dimensional algebras over a field, then the sufficient condition guarantees the existence of a stable equivalence of Morita type. In this way, we extend the classical result of Rickard. Furthermore, we provide several inductive methods for constructing those derived equivalences that induce stable equivalences of Morita type. It turns out that we may produce a lot of (usually not self-injective) finite-dimensional algebras that are both derived-equivalent and stably equivalent of Morita type; thus, they share many common invariants.
Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case
Authors: Nakanishi Tomoki 
Published: July 2016

AbstractThe dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have been partly proved by various authors. We prove these identities in full generality for any pair of Dynkin diagrams of simply laced type based on the cluster algebra formulation of the Y-systems.
A cohomological Tamagawa number formula
Authors: Huber Annette , Kings Guido 
Published: July 2016

AbstractFor smooth linear group schemes over ℤ, we give a cohomological interpretation of the local Tamagawa measures as cohomological periods. This is in the spirit of the Tamagawa measures for motives defined by Bloch and Kato. We show that in the case of tori, the cohomological and the motivic Tamagawa measures coincide, which proves again the Bloch-Kato conjecture for motives associated to tori.
The rationality problem for norm one tori
Authors: Endo Shizuo 
Published: July 2016

AbstractWe consider the problem of whether the norm one torus defined by a finite separable field extensionK/kis stably (or retract) rational overk. This has already been solved for the case whereK/kis a Galois extension. In this paper, we solve the problem for the case whereK/kis a non-Galois extension such that the Galois group of the Galois closure ofK/kis nilpotent or metacyclic.
Harmonic morphisms applied to classical potential theory
Authors: Fuglede Bent 
Published: July 2016

AbstractIt is shown that ifϕdenotes a harmonic morphism of type Bl between suitable Brelot harmonic spacesXandY, then a functionf, defined on an open setV ⊂ Y, is superharmonic if and only iff ∘ ϕis superharmonic onϕ–1(V) ⊂ X. The “only if” part is due to Constantinescu and Cornea, withϕdenoting any harmonic morphism between two Brelot spaces. A similar result is obtained for finely superharmonic functions defined on finely open sets. These results apply, for example, to the case whereϕis the projection from ℝNto ℝn(N &gt; n ≥1) or whereϕis the radial projection from ℝN\ {0} to the unit sphere in ℝN(N≥ 2).
Geometry of G2 orbits and isoparametric hypersurfaces
Authors: Miyaoka Reiko 
Published: July 2016

AbstractWe characterize the adjointG2orbits in the Lie algebragofG2as fibered spaces overS6with fibers given by the complex Cartan hypersurfaces. This combines the isoparametric hypersurfaces of case (g,m) = (6,2) with case (3,2). The fibrations on two singular orbits turn out to be diffeomorphic to the twistor fibrations ofS6andG2/SO(4). From the symplectic point of view, we show that there exists a 2-parameter family of Lagrangian submanifolds on every orbit.
Variation formulas for principal functions, II: Applications to variation for harmonic spans
Authors: Hamano Sachiko , Maitani Fumio , Yamaguchi Hiroshi 
Published: July 2016

AbstractA domainD⊂ Czadmits the circular slit mappingP(z) fora, b∈Dsuch thatP(z) – 1/(z–a) is regular ataandP(b) = 0. We callp(z) =log|P(z)|theLi-principal functionandα= log |P′(b)| theL1-constant, and similarly, the radial slit mappingQ(z) implies theL0-principal functionq(z) and theL0-constantβ. We calls=α–βtheharmonic spanfor (D, a, b). We show the geometric meaning ofs. Hamano showed the variation formula for theL1-constantα(t) for the moving domainD(t) in Czwitht∈B:= {t∈ C: |t| &lt;ρ}. We show the corresponding formula for theL0-constantβ(t) forD(t) and combine these to prove that, if the total spaceD =∪t∈B(t, D(t)) is pseudoconvex inB× Cz, thens(t) is subharmonic onB. As a direct application, we have the subharmonicity of log coshd(t) onB, whered(t) is the Poincaré distance betweenaandbonD(t).
Ordinary varieties and the comparison between multiplier ideals and test ideals
Authors: Mustaţă Mircea , Srinivas Vasudevan 
Published: July 2016

AbstractWe consider the following conjecture: ifXis a smooth and irreduciblen-dimensional projective variety over a fieldkof characteristic zero, then there is a dense set of reductionsXsto positive characteristic such that the action of the Frobenius morphism onHn(Xs, OXs) is bijective. There is another conjecture relating certain invariants of singularities in characteristic zero (the multiplier ideals) with invariants in positive characteristic (the test ideals). We prove that the former conjecture implies the latter one in the case of ambient nonsingular varieties.
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
Authors: Degtyarev Alex , Salepci Nermin 
Published: July 2016

AbstractWe address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz fibration is algebraic.
Sally’s question and a conjecture of shimoda
Authors: Goto Shiro , O’carroll Liam , Planas-Vilanova Francesc 
Published: July 2016

AbstractIn 2007, Shimoda, in connection with a long-standing question of Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete intersections, has Krull dimension at most 2. In this paper, having reduced the conjecture to the case of dimension 3, if the ring is regular and local of dimension 3, we explicitly describe a family of prime ideals of height 2 minimally generated by three elements. Weakening the hypothesis of regularity, we find that, to achieve the same end, we need to add extra hypotheses, such as completeness, infiniteness of the residue field, and the multiplicity of the ring being at most 3. In the second part of the paper, we turn our attention to the category of standard graded algebras. A geometrical approach via a double use of a Bertini theorem, together with a result of Simis, Ulrich, and Vasconcelos, allows us to obtain a definitive answer in this setting. Finally, by adapting work of Miller on prime Bourbaki ideals in local rings, we detail some more technical results concerning the existence in standard graded algebras of homogeneous prime ideals with an (as it were) excessive number of generators.
Toric degenerations of integrable systems on Grassmannians and polygon spaces
Authors: Nohara Yuichi , Ueda Kazushi 
Published: July 2016

AbstractWe introduce a completely integrable system on the Grassmannian of 2-planes in ann-space associated with any triangulation of a polygon withnsides, and we compute the potential function for its Lagrangian torus fiber. The moment polytopes of this system for different triangulations are related by an integral piecewise-linear transformation, and the corresponding potential functions are related by its geometric lift in the sense of Berenstein and Zelevinsky.
Generalized Lyubeznik numbers
Authors: Núñez-Betancourt Luis , Witt Emily E. 
Published: July 2016

AbstractGiven a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers but captures finer information. Thesegeneralized Lyubeznik numbersare defined in terms ofD-modules and are proved well defined using a generalization of the classical version of Kashiwara’s equivalence for smooth varieties; we also give a definition for finitely generatedK-algebras. These new invariants are indicators ofF-singularities in characteristicp &gt;0 and have close connections with characteristic cycle multiplicities in characteristic zero. We characterize the generalized Lyubeznik numbers associated to monomial ideals and compute examples of those associated to determinantal ideals.
Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation
Authors: Randriambololona Serge 
Published: July 2016

AbstractThis article presents two constructions motivated by a conjecture of van den Dries and Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct maximal polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.
On the Fundamental Existence Theorem of Kishi
Authors: Nakai Mitsuru 
Published: July 2016

Let Ω be a locally compact Hausdorff space and G(x, y) be a strictly positive lower semicontinuous function on the product space Ω×Ω of Ω. Such a function G(x, y) is called a kernel on Ω. The adjoint kernel Ğ(x, y) of G(x, y) is defined by Ğ(x, y) =G(y, x). Whenever we say a measure on Ω, we mean a positive regular Borel measure on Ω. The potential Gμ(x) and the adjoint potential Ğμ(x) of a measure μ relative to the kernel G(x, y) is defined byrespectively. These are also strictly positive lower semicontinuous functions on Ω provided μ≠0.
Faithfully Exact Functors and Their Applications to Projective Modules and Injective Modules
Authors: Ishikawa Takeshi 
Published: July 2016

The aim of this paper is to study a property of a special kind of exact functors and give some applications to projective modules and injective modules.In section 1 we introduce the notion of faithfully exact functors [Definition 1] as a generalization of the functor T(X) = X⊗M, where M is a faithfully flat module, and give a property of this class of functors [Theorem 1.1]. Next, applying this general theory to functors ⊗ and Horn, we define the notion of faithfully projective modules [Definition 2] and faithfully injective modules [Definition 3]. In the commutative case “faithfully projective” means, however, simply “projective and faithfully flat” [Proposition 2.3]. In section 2, equivalent conditions for a projective module P to be faithfully projective are given [Theorem 2.2, Proposition 2. 3 and 2.4]. And a simpler proof is given to Y. Hinohara’s result [6] asserting that projective modules over an indecomposable weakly noetherian ring are faithfully flat [Proposition 2.5]. In section 3, we consider faithfully injective modules.
Condensor Principle and the Unit Contraction
Authors: Itô Masayuki 
Published: July 2016

Deny introduced in [4] the notion of functional spaces by generalizing Dirichlet spaces. In this paper, we shall give the following necessary and sufficient conditions for a functional space to be a real Dirichlet space.Let be a regular functional space with respect to a locally compact Hausdorff space X and a positive measure ξ in X. The following four conditions are equivalent.
On a Class of Markov Processes Taking Values on Lines and the Central Limit Theorem
Authors: Fukushima Masatoshi , Hitsuda Masuyuki 
Published: July 2016

We shall consider a class of Markov processes (n(t), x(t)) with the continuous time parameter t∈e[0, ∞), whose state space is {1, 2,..., N}×R1. We shall assume that the processes are spacially homogeneous with respect to X∈R1. In detail, our assumption is that the transition functionFij(x,t) = P(n(t) = j, x(t)≦x|n(0) = i,x(0) = 0), t > 0, 1≦i, j,≦N, x∈R1satisfies following conditions (1, 1)~(1,4).
On Positive Solutions of the Heat Equation
Authors: Kato Masasumi 
Published: July 2016

Consider the positive and twice continuously differentiable solutions u of the heat equationin an open t-strip Ω = Rn×(0,T) for some T>0, where Rn is the n-dimensional Euclidean space.In this note, we prove a theorem of Fatou type on u and, as its application, the uniqueness theorem for the Cauchy problem of ( 1 ).
Spiral Asymptotic Values of Functions Meromorphic in the Unit Disk
Authors: Stebbins J.L. 
Published: July 2016

This paper contains part of the author’s Ph.D. dissertation directed by Frederick Bagemihl at Wayne State University. The research was supported by a grant from the Michigan Institute of Science and Technology.Alice Roth has made an extensive study of entire meromorphic functions with prescribed behavior along half rays emanating from the origin (6). The question arose whether analogous results could be found for functions meromorphic in the unit disk with the same behavior prescribed along an exhaustive class of spirals emanating from the origin. In this paper, I present a class of spirals which satisfactorily fills this role. However, I make no claim to the effect that only this class will suffice.
Sur l’ensemble d’Adherence Fine des Fonctions Algebroides
Authors: Toda Nobushige 
Published: July 2016

Dans ce mémoire, on fera pour les fonctions algébroïdes des études analogues à ceux des fonctions méromorphes dans |z|<∞ faits dans Doob [3], Toda [7].Soit g(z) une fonction méromorphe dans |Z|<∞ ayant un point singulier essentiel isolé à l’infini. J.L. Doob a obtenu le théorème suivant en utilisant la topologie fine pour g(z).
On a Class of Metrical Automorphisms on Gaussian Measure Space
Authors: Nomoto Hisao 
Published: July 2016

Let E be an infinite dimensional real nuclear space and H be its completion by a continuous Hilbertian norm ║ ║ of E. Then we have the relationwhere E* is the conjugate space of E. Consider a function C(ξ) on E defined by the formula(1)
Some Remarks on Evaluations of the Primitive Logic
Authors: Ono Hiroakira 
Published: July 2016

In [4], K. Ono introduced the notion of evaluations of the primitive logic LO and proved that any semi-evaluation E is an evaluation of LO if E satisfies the following conditions:
(E1) p* → 0 = 0,(E2) p* → p* = 0,(E3) 0 → p* = p*,(E4) p* → (p* → q*) = p* → q*,(E5) p* → (q* → r*) = q* → (p* → r*),(E6) p* → q* = 0 implies (r* → p*) → (r* → q*) = 0,(E7) (x)p*(x) → p*(t) = 0 for any t, and(E8) if u* → p*(t) = 0 for any t, then u* → (x)p*(x) = 0.
Propriétés des Solutions Faibles Non Négatives de L’équation Parabolique
Authors: Chabrowski J. 
Published: July 2016

Le but de cette communication est de prouver que la solution u(t, x) faible non négative dans (0,T]=En de l’équationpossède la limite presque partout dans En si t converge vers zéro, ainsi qu’elle représentable sous la forme d’une intégrale de la solution fondamentale faible de (1) par rapport à une mesure non négative. Ces problèmes ont été traités par M. Kato et M. Krzyzanski (voir [7] et [8]) pour les solutions au sens classiques. Nos démonstrations sont basées sur les méthodes utilisées dans leurs travaux.
Boundary Conditions for the Heat Equation in a Several-Dimensional Region
Authors: Gallavotti G. , McKean H. P. 
Published: July 2016

AbstractThe heat equation is to be solved in a severaldimensional region D with on the boundary B of D. The elementary solution (Green’s function) is interpreted as the transition density of an associated Brownian motion. The latter is built up pathwise from the free Brownian motion by simple geometric and probabilistic transformations.
Zur Isoperimetrischen Ungleichung für k-Dimensionale Konvexe Polyeder
Authors: Hadwiger H. 
Published: July 2016

Für ein eigentliches konvexes Polyeder P des k-dimensionalen euklidischen Raumes gilt die isoperimetrische Ungleichung(1) wobei V das Volumen und F die Oberfläche von P bedeuten; die Grôsse wk bezeichnet das Volumen der k-dimensionalen Einheitskugel, also(2)
Boundary Isomorphism between Dirichlet Finite Solutions of Δu = Pu and Harmonic Functions
Authors: Singer Ivan J. 
Published: July 2016

Consider an open Riemann surface R and a density P(z)dxdy (z = x + iy), well defined on R. As was shown by Myrberg in [3], if P ≢ 0 is a nonnegative α-Hölder continuous density on R (0 < α ≤ 1) then there exists the Green’s functions of the differential equationp>on R, where Δ means the Laplace operator. As a consequence, there always exists a nontrivial solution on R.
Bäcklund transformations of the first kind associated with Monge-Ampère’s equations
Authors: Matsuda Michihiko 
Published: July 2016

Due to Clairin and Goursat, a Bäcklund transformation of the first kind can be associated with Monge-Ampère’s equation. We shall consider Monge-Ampère’s equation of the form s + f(x, y, z, p, q) + g(x, y, z, p, q) t = 0, where p = ∂z/∂x, q = ∂z/∂y, s = ∂2z/∂x∂y, t = ∂2z/∂y2. The following theorems will be obtained:1. The transformed equation takes on the same form s′ + f′ + g′t′ = 0 if and only if the given equation can be transformed to a Teixeira equation s + L(x, y, z, q)t + M(x, y, z, q)p + N(x, y, z, q) = 0 by a contact transformation.2. Teixeira equation s + tL + pM + N = 0 is solved by integrable systems of order n if and only if the transformed equation is solved by integrable systems of order n — 1.
Normal subgroups of finite multiply transitive permutation groups
Authors: Bannai Eiichi 
Published: July 2016

Wagner [5] and Ito [2] proved the following theorems respectively.THEOREM OF WAGNER. Let G be a triply transitive permutation group on a set Ω = {1,2, …, n}, and let n be odd and n > 4. If H is a normal subgroup (≠1) of G, then H is also triply transitive on Ω.
On Lie algebras of vector fields with invariant submanifolds
Authors: Koriyama Akira 
Published: July 2016

It is known (Pursell and Shanks [9]) that an isomorphism between Lie algebras of infinitesimal automorphisms of C∞ structures with compact support on manifolds M and M′ yields an isomorphism between C∞ structures of M and M’.Omori [5] proved that this is still true for some other structures on manifolds. More precisely, let M and M′ be Hausdorff and finite dimensional manifolds without boundary. Let α be one of the following structures:
On the distribution of zeros of a strongly annular function
Authors: Osada Akio 
Published: July 2016

A functionf(z), regular in the unit diskD, is called annular ([1], p. 340) if there is a sequence of closed Jordan curvesJn⊂Dsatisfying(A1)Jnis contained in the interior ofJn+1for everyn,(A2)givenε> 0, there exists a positive numbern(ε)such that, for eachn > n(ε), Jnlies in the region 1 –ε< |z| < 1 and(A3)lim min {|f(z)|;z ∈ Jn} = + ∞.
A note on grade
Authors: Jothilingam P. 
Published: July 2016

All rings that occur in this note will be assumed to be commutative with unity and all modules will be finitely generated and unitary.The grade of a module M over a noetherian local ring R is defined to be the length of a maximal R-sequence contained in the annihilator of M. If M has finite projective dimension it is well-known that grade M ≤ proj. dim M. We can say more when R is a regular local ring.
Two theorems on excellent rings
Authors: Greco Silvio 
Published: July 2016

Let f: A → B be a homomorphism of commutative noetherian rings. The main results of this paper are:(a) Assume f is finite and induces a surjective map on the spectra. Then if B is quasi-excellent A is quasi-excellent and is excellent if it is universally catenarian (Th. 3.1); and(b) If f is absolutely flat and A is excellent then B is excellent (Th. 5.3). In particular the strict henselization of an excellent local ring is excellent (Cor. 5.6.).
The fourth dimension subgroups and polynomial maps, II
Authors: Tahara Ken-Ichi 
Published: July 2016

In our previous paper [3] we proved the following ([3, Theorem 16]) :THEOREM A. Let G be a 2-group of class 3. Let G2 and G/G2 be direct products of cyclic groups 〈yq〉 of order αq (1 ≦ q ≦ m), and of cyclic groups 〈hi〉 of order βi (1 ≦ i ≦ n) with β1 ≧ β2 ≧ · · · βn, respectively. Let xi be representatives of hi (1 ≦ i ≦ n), and put Then a homomorphism ψ:G3→T can be extended to a polynomial map from G to T of degree ≦ 4 if and only if there exists an integral solution in the following linear equations of Xiq (1 ≦ i ≦ n, 1 ≦ q ≦ m) with coefficients in T:	(I)where δij is the Kronecker symbol for βi: i.e. δij = 1 or 0 according to βi = βj or βi > βj, respectively.
Algebras With Vanishing n-Cohomology Groups
Authors: Ikeda Masatoshi , Nagao Hiroshi , Nakayama Tadashi 
Published: July 2016

Cohomology theory for (associative) algebras was first established in general higher dimensionalities by G. Hochschild [3], [4], [5]. Algebras with vanishing 1-cohomology groups are separable semisimple algebras ([3], Theorem 4.1). On extending and refining our recent results [6], [8], [12], we establish in the present paper the following:Let n ≧ 2. Let A be an (associative) algebra (of finite rank) possessing a unit element 1 over a field Ω, and N be its radical.
On Associative Compositions in Finite Nilpotent Groups
Authors: Iwahori Nagayosi , Hattori Akira 
Published: July 2016

Let(1) be a word in two variables X, Y, i.e. an element in the free group F2 on two generators X, Y. Let us say that f defines an associative composition for a group G if for arbitrary elements a, b, c in G we have(2) where a ° b is defined by(3)
Tensor products of positive definite quadratic forms IV
Authors: Kitaoka Yoshiyuki 
Published: July 2016

Let L, M, N be positive definite quadratic lattices over Z. We treated the following problem in [5], [6]:If L ⊗ M is isometric to L ⊗ N, then is M isometric to N?We gave a condition (**) in [6] such that the answer is affirmative for an indecomposable lattice L satisfying (**), and we gave some examples. In this paper we introduce a certain apparently weaker condition (A) than the condition (**), and we show that the condition (A) implies the condition (**) and more on integral orthogonal groups than a result in [6].
A note on Thom classes in general cohomology
Authors: Haas Ronald Kirk , Uehara Hiroshi 
Published: July 2016

This note is dedicated to the second author’s teacher, Professor Atsuo Komatsu, in celebration of his seventieth birthday.It is well known [4], [7] that the theory of characteristic classes in general cohomology is essentially based upon one theorem, the Leray-Hirsch Theorem. We further claim [8] that the entire theory could be developed merely from the Künneth Formula if under suitable conditions a truly relative version of the Meyer-Vietoris sequence exists in the general cohomology theory. In his lectures delivered at Aarhus in 1968, Dold [6] set up the necessary machinery including the Leray-Hirsch Theorem to define Chern Classes with values in general cohomology. However, he then stated [6, p. 47] that he “found a difficulty here in choosing adequate orientations (Thorn Classes) for the bundles involved”, and proceeded differently, discarding the “classical” approach used in both ordinary cohomology [9] and K-theory [3]. Later, he [7] published a more categorical work, although the approach to Chern Classes was basically unchanged from his previous work. Consequently, the possibility of the classical direct approach to the theory has remained open.
The canonical modules of graded rings defined by generic matrices
Authors: Yoshino Yuji 
Published: July 2016

Let k be a field, and X = [xij] be an n × (n + m) matrix whose elements are algebraically independent over k.We shall study the canonical module of the graded ring R, which is a quotient ring of the polynomial ring A = k[X] by the ideal αn(X) generated by all the n × n minors of X.