Search

In this paper, we generalize the idea of Song, Zhao and Huang [Czechoslov. Math. J., 70, 483–504 (2020)] and introduce the notion of right (left) Gorenstein subcategory r G (C , D) (l G (C , D)) , relative to two additive full subcategories C and D of an abelian category A . Under the assumption that C ⊆ D , we prove that the right Gorenstein subcategory r G (C , D) possesses many nice properties that it is closed under extensions, kernels of epimorphisms and direct summands. When C ⊆ D and C ⊥ D , we show that the right Gorenstein subcategory r G (C , D) admits some kind of stability. Then we discuss a resolution dimension for an object in A , called r G (C , D) -projective dimension. Finally, we prove that if (U , V) is a hereditary cotorsion pair with kernel C has enough injectives, such that U ⊆ D and U ⊥ D , then (r G (C , D) , r e s C ^ , C) is a weak Auslander—Buchweitz context, where res C ^ is the subcategory of A consisting of objects with finite C -projective dimension. [ABSTRACT FROM AUTHOR]

In this paper, we characterize that the boundedness, compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space. This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the Bergman space due to Stroethoff and Zheng's paper [Trans. Amer. Math. Soc., 354, 2495–2520 (2002)]. [ABSTRACT FROM AUTHOR]

Zhao and Ho asked in a recent paper that for each T0 space X, whether KB(X) (the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Topκ of the category Top0 of T0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Topκ. [ABSTRACT FROM AUTHOR]

This paper contains two parts toward studying abelian varieties from the classification point of view. In a series of papers [Doc. Math., 21, 1607–1643 (2016)], [Taiwanese J. Math., 20(4), 723–741 (2016)], etc., the current authors and T. C. Yang obtain explicit formulas for the numbers of superspecial abelian surfaces over finite fields. In this paper, we give an explicit formula for the size of the isogeny class of simple abelian surfaces with real Weil number √q. This establishes a key step that extends our previous explicit calculation of superspecial abelian surfaces to those of supersingular abelian surfaces. The second part is to introduce the notion of genera and idealcomplexes of abelian varieties with additional structures in a general setting. The purpose is to generalize the previous work by the second named author [Forum Math., 22(3), 565–582 (2010)] on abelian varieties with additional structures to similitude classes, which establishes more results on the connection between geometrically defined and arithmetically defined masses for further investigations. [ABSTRACT FROM AUTHOR]

In 2010, Gábor Czédli and E. Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet [A cover-preserving embedding of semimodular lattices into geometric lattices. Advances in Mathematics, 225, 2455–2463 (2010)]. That is to say: What are the geometric lattices G such that a given finite semimodular lattice L has a cover-preserving embedding into G with the smallest ∣G∣? In this paper, we propose an algorithm to calculate all the best extending cover-preserving geometric lattices G of a given semimodular lattice L and prove that the length and the number of atoms of every best extending cover-preserving geometric lattice G equal the length of L and the number of non-zero join-irreducible elements of L, respectively. Therefore, we solve the problem on the best cover-preserving embedding of a given semimodular lattice raised by Gábor Czédli and E. Tamás Schmidt. [ABSTRACT FROM AUTHOR]

Let ( T, d) be a dendrite with finite branch points and f be a continuous map from T to T. Denote by ω( x, f) and P( f) the ω-limit set of x under f and the set of periodic points of f, respectively. Write Ω( x, f) = { y| there exist a sequence of points x ∈ T and a sequence of positive integers n < n < ··· such that lim x = x and lim $$f^{n_{k}}$$ ( x ) = y}. In this paper, we show that the following statements are equivalent: (1) f is equicontinuous. (2) ω( x, f) = Ω( x, f) for any x ∈ T. (3) ∩ f ( T) = P( f), and ω( x, f) is a periodic orbit for every x ∈ T and map h: x → ω( x, f) ( x ∈ T) is continuous. (4) Ω( x, f) is a periodic orbit for any x ∈ T. [ABSTRACT FROM AUTHOR]

In this paper, under a similar but stronger condition than that of Ambrosetti and Rabinowitz we find a T-periodic solution of the autonomous superquadratic second order Hamiltonian system with even potential for any T > 0; moreover, such a solution has T as its minimal period. [ABSTRACT FROM AUTHOR]

In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ*-algebras for the following Cauchy-Jensen additive mapping: The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias’ stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300. This is applied to investigate isometric isomorphisms between proper CQ*-algebras. [ABSTRACT FROM AUTHOR]

A simple graph G is a 2-tree if G = K3, or G has a vertex v of degree 2, whose neighbors are adjacent, and G — v is a 2-tree. Clearly, if G is a 2-tree on n vertices, then E(G) = 2n — 3. A non-increasing sequence π = (d1,...,dn) of nonnegative integers is a graphic sequence if it is realizable by a simple graph G on n vertices. [Acta Math. Sin. Engl. Ser., 25, 795–802 (2009)] proved that if k ≥ 2, n ≥ and π = (d1,...,dn) is a graphic sequence with , then p has a realization containing every 1-tree (the usual tree) on k vertices. Moreover, the lower bound (k — 2)n is the best possible. This is a variation of a conjecture due to Erdos and Sós. In this paper, we investigate an analogue problem for 2-trees and prove that if k ≥ 3 is an integer with k = i (mod3), π = (d1,...,dn is a graphic sequence with , then π has a realization containing every 2-tree on k vertices. Moreover, the lower bound max is the best possible. This result implies a conjecture due to [Discrete Math. Theor. Comput. Sci., 17(3), 315–326 (2016)]. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the convergence problem of the iteration scheme x n+1 = λ n+1 y +(1–λ n+1) T n+1 x n for a family of infinitely many nonexpansive mappings T 1, T 2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results. [ABSTRACT FROM AUTHOR]

This paper considers the Steiner Minimal Tree (SMT) problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI: The rectilinear case corresponds to the currently used M-architecture, which uses either horizontal or vertical routing, while the octilinear case corresponds to a new routing technique, X-architecture, that is based on the pervasive use of diagonal directions. The experimental studies show that the X-architecture demonstrates a length reduction of more than 10–20%. In this paper, we make a theoretical study on the lengths of SMTs in these two planes. Our mathematical analysis confirms that the length reduction is significant as the previous experimental studies claimed, but the reduction for three points is not as significant as for two points. We also obtain the lower and upper bounds on the expected lengths of SMTs in these two planes for arbitrary number of points. [ABSTRACT FROM AUTHOR]

In a previous paper, we have described all reproductive general solutions of a Post equation, supposing that a general solution is known. In this paper we describe all general solutions of Post equation, supposing that a general solution of this equation is known (Theorem 6). As a special case we get the previous characterization of reproductive solutions and a similar result for Boolean equations (Theorem 9). [ABSTRACT FROM AUTHOR]

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained. [ABSTRACT FROM AUTHOR]

Assume that m ⩾ 2, p is a prime number, (m,p(p - 1)) = 1, -1 ∉ (p) ⊂ (∤/m∤)* and [(∤/m∤)* : (p)] = 4. In this paper, we calculate the value of Gauss sum G(X) = Σx∈F*qX(x)ζT(x)P over ...q, where q = pf, f = φ(m)/4, X is a multiplicative character of ...q and T is the trace map from ...q to ...p. Under our assumptions, G(X) belongs to the decomposition field K of p in ℚ(ζm) and K is an imaginary quartic abelian number field. When the Galois group Gal(K/ℚ) is cyclic, we have studied this cyclic case in another paper: "Gauss sums of index four: (1) cyclic case" (accepted by Acta Mathematica Sinica, 2003). In this paper we deal with the non-cyclic case. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang’s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems. [ABSTRACT FROM AUTHOR]

In this paper, some new generalizations of inverse type Hilbert-Pachpatte integral inequalities are proved. The results of this paper reduce to those of Pachpatte (1998, J. Math. Anal. Appl.226, 166–179) and Zhao and Debnath (2001, J. Math. Anal. Appl.262, 411–418). [ABSTRACT FROM AUTHOR]

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. [ABSTRACT FROM AUTHOR]

In this paper, we consider the weakly damped wave equations with hereditary effects, and the nonlinearity f satisfies critical growth. The delay term g(t, ut) may be driven by a function with very weak assumptions, namely, just measurability. We analyze the well-posedness of solutions and verify the existence of the pullback D-attractor in CH01(Ω)×CL2(Ω) by constructing the energy functional and combining with the idea of the contractive function. [ABSTRACT FROM AUTHOR]

In this paper, we present a local Csörgö-Révész type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Lévy’s modulus of continuity for Brownian motion. [ABSTRACT FROM AUTHOR]

Let S = ( a , ..., a ; b , ..., b ), where a , ..., a and b , ..., b are two nonincreasing sequences of nonnegative integers. The pair S = ( a , ..., a ; b , ..., b ) is said to be a bigraphic pair if there is a simple bipartite graph G = ( X ∪ Y, E) such that a , ..., a and b , ..., b are the degrees of the vertices in X and Y, respectively. Let Z be the cyclic group of order 3. Define σ( Z , m, n) to be the minimum integer k such that every bigraphic pair S = ( a , ..., a ; b , ..., b ) with a , b ≥ 2 and σ( S) = a + ⋯ + a ≥ k has a Z -connected realization. For n = m, Yin [ Discrete Math., 339, 2018-2026 (2016)] recently determined the values of σ( Z , m, m) for m ≥ 4. In this paper, we completely determine the values of σ( Z , m, n) for m ≥ n ≥ 4. [ABSTRACT FROM AUTHOR]

In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved. [ABSTRACT FROM AUTHOR]

In this paper, we obtain that a convex g evaluation can be dominated by the corresponding Choquet evaluation if and only if the g has the form g( t, y, z) = µ y+ h( t, z), where h( t, z) is positively homogeneous and subadditive with respect to z. [ABSTRACT FROM AUTHOR]

The backward heat equation is a typical ill-posed problem. In this paper, we shall apply a dual least squares method connecting Shannon wavelet to the following equation Motivated by Regińska's work, we shall give two nonlinear approximate methods to regularize the approximate solutions for high-dimensional backward heat equation, and prove that our methods are convergent. [ABSTRACT FROM AUTHOR]

In this paper, we express the essential norms of composition operators between weighted Bergman spaces of the unit disc in terms of the generalized Nevanlinna counting function. [ABSTRACT FROM AUTHOR]

In the present paper we obtain and extend the boundedness property of the Adams type for multilinear fractional integral operators. Also, we deal with the Olsen type inequality. [ABSTRACT FROM AUTHOR]

In this paper, the existence and multiplicity of a class of double resonant semilinear elliptic equations with the Dirichlet boundary value are studied. [ABSTRACT FROM AUTHOR]

This paper is concerned with the L- L estimates of the solutions for a class of pseudodifferential equations under some suitable degenerate assumptions. As applications, these estimates can be used to show that a generalized Schrödinger operator with some integrable potential generates a fractionally integrated group in L(ℝ). [ABSTRACT FROM AUTHOR]

proper total coloring of a graph G such that there are at least 4 colors on those vertices and edges incident with a cycle of G, is called acyclic total coloring. The acyclic total chromatic number of G is the least number of colors in an acyclic total coloring of G. In this paper, it is proved that the acyclic total chromatic number of a planar graph G of maximum degree at least k and without l cycles is at most Δ( G) + 2 if ( k, l) ∈ {(6, 3), (7, 4), (6, 5), (7, 6)}. [ABSTRACT FROM AUTHOR]

Two cellular embeddings i: G → S and j: G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h: S → S such that hi = j. The genus polynomial of a graph G is defined by where a is the number of equivalence classes of embeddings of G into the orientable surface S with g genera. In this paper, we compute the genus polynomial of a graph obtained from a cycle by replacing each edge by two multiple edges. [ABSTRACT FROM AUTHOR]

In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in ℝ n by employing the Li’s method of energy function. [ABSTRACT FROM AUTHOR]

In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta functions, and also re-derive the quintuple product identity, one of Ramanujan’s identities, Winquist’s identity and many other interesting identities. [ABSTRACT FROM AUTHOR]

In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm L p (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. [ABSTRACT FROM AUTHOR]

This paper studies relationships between the best linear unbiased estimators (BLUEs) of an estimable parametric functions K β under the Gauss-Markov model { y, X β, σ2 Σ} and its misspecified model { y, X0 β, σ2 Σ0}. In addition, relationships between BLUEs under a restricted Gauss-Markov model and its misspecified model are also investigated. [ABSTRACT FROM AUTHOR]

In this paper we study zero-sum stochastic games. The optimality criterion is the long-run expected average criterion, and the payoff function may have neither upper nor lower bounds. We give a new set of conditions for the existence of a value and a pair of optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature, and some new sufficient conditions for the existence of a pair of optimal stationary strategies are imposed on the primitive data of the model. Our results are illustrated with a queueing system, for which our conditions are satisfied but some of the conditions in some previous literatures fail to hold. [ABSTRACT FROM AUTHOR]

In this paper, properties of the entropic risk measure are examined rigorously in a general framework. This risk measure is then applied in a dynamic portfolio optimization problem, appearing in the risk management constraint. By considering the dual problem, we prove the existence and uniqueness of the solution and obtain an analytic expression for the solution. [ABSTRACT FROM AUTHOR]

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L p metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the following implicit iteration scheme recently introduced by Xu and Ori [ Numer. Funct. Anal. Optim., 22, (2001) 767–773]: and to prove several strongly and weakly convergent theorems of the iteration for a finite family of pseudocontractive mappings under condition α n ∈ (0, b] ⊂ (0, 1). [ABSTRACT FROM AUTHOR]

This paper considers the isometric extension problem concerning the mapping from the unit sphere S 1( E) of the normed space E into the unit sphere S 1( l ∞(Γ)). We find a condition under which an isometry from S 1( E) into S 1( l ∞(Γ)) can be linearly and isometrically extended to the whole space. Since l ∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are solved. More precisely, if E and F are two normed spaces, and if V 0: S 1( E) → S 1( F) is a surjective isometry, where c 00(Γ) ⊆ F ⊆ l ∞(Γ), then V 0 can be extended to be an isometric operator defined on the whole space. [ABSTRACT FROM AUTHOR]

This paper proves that, for any generator x ε Ext ( Z p , Z p ), if (1 L ⋀ i)*φ*( x) ε Ext ( H*L ⋀ M, Z p ) is a permanent cycle in the Adams spectral sequence (ASS), then h0 x ε Ext ( Z p , Z p ) also is a permenent cycle in the ASS. As an application, the paper obtains that h 0 h n h m ∈ $$ Ext_A^{3,p^n q + p^m q + q} (Z_p ,Z_p ) $$ is a permanent cycle in the ASS and it converges to elements of order p in the stable homotopy groups of spheres $$ \pi _{p^n q + p^m q + q - 3} S $$ , where p ≥ 5 is a prime, s ≤ 4, n ≥ m+2 ≥ 4 and M is the Moore spectrum. [ABSTRACT FROM AUTHOR]

We make a further advance concerning the maximum principle for second-order elliptic operators. We investigate in particular a geometric condition, first considered by Berestycki–Nirenberg– Varadhan, that seems to be natural in view of the application of the boundary weak Harnack inequality, on which our argument is based. Setting it free from some technical assumptions, apparently needed in earlier papers, we significantly enlarge the class of unbounded domains where the maximum principle holds, compatibly with the first-order term. [ABSTRACT FROM AUTHOR]

This paper addresses the construction of wavelet frame from a frame multiresolution analysis ( FMRA) associated with a dilation matrix of determinant ±2. The dilation matrices of determinant ±2 can be classified as six classes according to integral similarity. In this paper, for four classes of them, the construction of wavelet frame from an FMRA is obtained, and, as examples, Shannon type wavelet frames are constructed, which have an independent value for their optimality in some sense. [ABSTRACT FROM AUTHOR]

Liu and Yan gave the degree condition for a balanced bipartite graph G = ( V 1, V 2; E) to have k vertex–disjoint quadrilaterals containing any given k independent edges e 1, . . . , e k of G, respectively. They also conjectured that for any k independent edges e 1, . . . , e k of G, G has a 2–factor with k cycles C 1, C 2, . . . , C k with respect to { e 1, e 2, . . . , e k } such that k–1 of them are quadrilaterals. In this paper, we prove this conjecture. [ABSTRACT FROM AUTHOR]

Suppose F is a field different from F2, the field with two elements. Let Mn (F) and Sn (F) be the space of n × n full matrices and the space of n × n symmetric matrices over F, respectively. For any G1, G2 ∈ {Sn (F), Mn (F)} , we say that a linear map f from G1 to G2 is inverse-preserving if f(X)-1 = f(X-1) for every invertible X ∈ G1. Let ... (G1, G2) denote the set of all inverse-preserving linear maps from G1 to G2. In this paper the sets ... (Sn (F), Mn (F)), ... (Sn (F), Sn (F)), ... (Mn (F), Mn(F)) and are characterized. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following results: 1) A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2) The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr(α²) = 1, where α generates N; 3) An optimal normal basis N is self-dual if and only if N is a type-I optimal normal basis with q = n = 2 or N is a type-II optimal normal basis. [ABSTRACT FROM AUTHOR]

We will show in this paper that if λ is very close to 1, then can be attained, where M is a compact–manifold with boundary. This result gives a counter–example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" ( Comm. Pure. Appl. Math., 55, 135–152, 2002). [ABSTRACT FROM AUTHOR]

In this paper, we shall present a short and simple proof on the isometric linear extension problem of into–isometries between two unit spheres of atomic abstract L p –spaces (0 < p < ∞). [ABSTRACT FROM AUTHOR]

In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C0(Ω0). As a corollary, we show that there is no ∈–isometry from any abstract M space with a strong unit into C0(Γ) if $$ 0 < \in < \frac{1} {9}. $$ [ABSTRACT FROM AUTHOR]

Inclines are the additively idempotent semirings in which products are less than or equal to either factor. In this paper, some necessary and sufficient conditions for a matrix over L to be invertible are given, where L is an incline with 0 and 1. Also it is proved that L is an integral incline if and only if GL n( L) = PL n( L) for any n ( n ≥ 2), in which GL n( L) is the group of all n × n invertible matrices over L and PL n( L) is the group of all n × n permutation matrices over L. These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive (weak) solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition. [ABSTRACT FROM AUTHOR]

The existence, multiplicity and infinite solvability of positive solutions are established for some two–point boundary value problems of one–dimensional p–Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number. [ABSTRACT FROM AUTHOR]