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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]

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]

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]

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]

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]

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 ( 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]

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 investigate the intersection numbers of nearly Kirkman triple systems. J [ v] is the set of all integers k such that there is a pair of NKTS( v)s with a common uncovered collection of 2-subset intersecting in k triples. It has been established that $${J_N}\left[ v \right] = \left\{ {0,1,...,\frac{{v\left( {v - 2} \right)}}{6} - 6,\frac{{v\left( {v - 2} \right)}}{6} - 4,\frac{{v\left( {v - 2} \right)}}{6}} \right\}$$ for any integers v = 0 (mod 6) and v ≥ 66. For v ≤ 60, there are 8 cases left undecided. [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]

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]

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]

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]

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]

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 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]

In this paper, we prove that a product F × F of saturated fusion systems is exotic if and only if at least one of the factors is exotic. This result provides a method to construct new exotic fusion systems by known exotic fusion systems. We also investigate central products of saturated fusion systems. [ABSTRACT FROM AUTHOR]

In this paper, by using the parametric representation of spirallike mappings, we construct to obtain the growth theorem of spirallike mappings on Reinhardt domain B. Moreover, the distortion theorem of spirallike mappings is obtained. [ABSTRACT FROM AUTHOR]

By Petersen's Theorem, a bridgeless cubic graph has a 2-factor. Fleischner ( Discrete Math., 101, 33-37 (1992)) has extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has an even factor without isolated vertices. Let m > 0 be even and m > 0 be odd. In this paper, we prove that every m-edge-connected graph with minimum degree at least m + 1 contains an even factor with minimum degree at least m and every ( m + 1)-edge-connected graph contains an odd factor with minimum degree at least m, which further extends Fleischner's result. Moreover, we show that our results are best possible. [ABSTRACT FROM AUTHOR]

For 0 < p < 1, Haberl and Ludwig defined the notions of symmetric L-intersection body and nonsymmetric L-intersection body. In this paper, we introduce the general L-intersection bodies. Furthermore, the Busemann-Petty problems for the general L-intersection bodies are shown. [ABSTRACT FROM AUTHOR]

For positive numbers j and k, an L( j, k)-labeling f of G is an assignment of numbers to vertices of G such that | f( u) − f( v)| ≥ j if uv ∈ E( G), and | f( u) − f( v)| ≥ k if d( u, v) = 2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L( j, k)-number of G, denoted by λ( G), is the minimum span over all L( j, k)-labelings of G. In this paper, we give some results about the L( j, k)-number of the direct product of a path and a cycle for j ≤ k. [ABSTRACT FROM AUTHOR]

In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations. [ABSTRACT FROM AUTHOR]

A labeling f of a graph G is a bijection from its edge set E( G) to the set {1, 2, ..., | E( G)|}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K2 is antimagic. In this paper, we show that if G is an n-vertex graph with minimum degree at least r, and G2 is an m-vertex graph with maximum degree at most 2 r − 1 ( m ≥ n), then G ∀ G is antimagic. [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 prove the existence of a uniform attractor for non-autonomous Brinkman-Forchheimer equations with general delay and time-dependent external force. [ABSTRACT FROM AUTHOR]

In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature. [ABSTRACT FROM AUTHOR]

In this paper, we prove Beurling's theorem for NA groups, from which we derive some other versions of uncertainty principles. [ABSTRACT FROM AUTHOR]

In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin( v) = {( s, t): ∃ a pair of maximum kite packings of order v intersecting in s blocks and s + t triangles}. Let Adm( v) = {( s, t): s + t ≤ b, s, t are non-negative integers}, where b = └ v ( v −1)/8┘. It is established that Fin( v) = Adm( v)\{( b− 1, 0), ( b − 1, 1)} for any integer v ≡ 0,1 (mod 8) and v ≥ 8; Fin( v) = Adm( v) for any integer v ≡ 2, 3, 4, 5, 6,7 (mod 8) and v ≥ 4. [ABSTRACT FROM AUTHOR]

Let $$\mathcal{A}$$ and $$\mathcal{B}$$ be unital rings, and $$\mathcal{M}$$ be an $$\left( {\mathcal{A},\mathcal{B}} \right)$$-bimodule, which is faithful as a left $$\mathcal{A}$$-module and also as a right $$\mathcal{B}$$-module. Let $$\mathcal{U} = Tri\left( {\mathcal{A},\mathcal{M},\mathcal{B}} \right)$$ be the triangular algebra. In this paper, we give some different characterizations of Lie higher derivations on $$\mathcal{U}$$. [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]

Let $$\mathbb{S}$$ be a periodic set in ℝ and $$L^2 \left( \mathbb{S} \right)$$ be a subspace of L(ℝ). This paper investigates the density problem for multiwindow Gabor systems in $$L^2 \left( \mathbb{S} \right)$$ for the case that the product of timefrequency shift parameters is a rational number. We derive the density conditions for a multiwindow Gabor system to be complete (a frame) in $$L^2 \left( \mathbb{S} \right)$$. Under such conditions, we construct a multiwindow tight Gabor frame for $$L^2 \left( \mathbb{S} \right)$$ with window functions being characteristic functions. We also provide a characterization of a multiwindow Gabor frame to be a Riesz basis for $$L^2 \left( \mathbb{S} \right)$$, and obtain the density condition for a multiwindow Gabor Riesz basis for $$L^2 \left( \mathbb{S} \right)$$. [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]

It is well known that the convergence of multivariate subdivision schemes with finite masks can be characterized via joint spectral radius. For nonnegative masks, we will present in this paper some computable simply sufficient conditions for the convergence, which will cover a substantially large class of schemes. [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, we introduce the concept of VT-congruence triples on a regular semigroup S and show how such triples can be constructed by using the equivalences on S/ℒ, S/R and the special congruences on S. Also, such congruence triples are characterized so that an associated congruence can be uniquely determined by a given congruence triple. Moreover, we also consider the VH-congruence pairs on an orthocryptogroup. [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]

In this paper, we show that all the nontrivial valuations on surfaces can be given by the infinite sequences of blowing-ups, and give the process of blowing-ups. [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]