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Abstract Some cases of the LFED Conjecture, proposed by the second author [15] , for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions k (x) of the polynomial algebra k [ x ] , the formal power series algebra k [ [ x ] ] and the Laurent formal power series algebra k [ [ x ] ] [ x − 1 ] , where x = (x 1 , x 2 , ... , x n) denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized. [ABSTRACT FROM AUTHOR]

Abstract We study the differential identities of the algebra U T 2 of 2 × 2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L = Der (U T 2) of derivations of U T 2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group S n and we determine the decomposition of the corresponding character into irreducibles. If V is the variety of differential algebras generated by U T 2 , we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almost polynomial growth. [ABSTRACT FROM AUTHOR]

Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract Let R ⊆ Q be rings such that the inclusion φ : R → Q is an epimorphism in the category of rings and Q is flat both as a right and as a left R -module. Assume that F. dim (Q Q ) = 0 , that is, that every left Q -module has projective dimension 0 or ∞. We prove that the following conditions are equivalent: (i) Flat left R -modules are strongly flat. (ii) Matlis-cotorsion left R -modules are Enochs-cotorsion. (i i i) h -divisible left R -modules are weak-injective. (iv) Homomorphic images of weak-injective left R -modules are weak-injective. (v) Homomorphic images of injective left R -modules are weak-injective. (vi) Left R -modules of weak dimension ≤1 are of projective dimension ≤1. (vii) The cotorsion pairs (P 1 , H D) and (F 1 , W I) coincide. Moreover, if R is a right and left Ore ring, S is its set of regular elements and Q = R [ S − 1 ] = [ S − 1 ] R is the classical ring of quotients of R , then the seven conditions above are also equivalent to: (v i i i) Divisible left R -modules are weak-injective. This extends a result by Fuchs and Salce (2018) [10] for modules over a commutative ring R. [ABSTRACT FROM AUTHOR]

Abstract Let g E H be the Eguchi–Hanson metric on the blow-up of ℂ 2 at the origin. In this paper we show that m g E H is not balanced for any positive integer m. [ABSTRACT FROM AUTHOR]

Abstract An interval matrix is a matrix whose entries are intervals in R. Let p , q ∈ N ∖ { 0 } and let α = ([ α _ i , j , α ‾ i , j ]) i , j be a p × q interval matrix; given a p × q matrix A with entries in R , we say that A ∈ α if a i , j ∈ [ α _ i , j , α ‾ i , j ] for any i , j. We establish a criterion to say if an interval matrix contains a matrix of rank 1. Moreover we determine the maximum rank of the matrices contained in a given interval matrix. Finally, for any interval matrix α with no more than 3 columns, we describe a way to find the range of the ranks of the matrices contained in α . [ABSTRACT FROM AUTHOR]

Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]

We investigate the connection between conditional local limit theorems and the local time of integer-valued stationary processes. We show that a conditional local limit theorem (at 0) implies the convergence of local times to Mittag-Leffler distributions, both in the weak topology of distributions and a.s. in the space of distributions. [ABSTRACT FROM AUTHOR]

Let X be an irreducible smooth projective curve, defined over an algebraically closed field k , of genus at least three and L a line bundle on X . Let M X ( r , L ) be the moduli space of stable vector bundles on X of rank r and determinant L with r ≥ 2 . We prove that the Brauer group Br ( M X ( r , L ) ) is cyclic of order g . c . d . ( r , degree ( L ) ) . We also prove that Br ( M X ( r , L ) ) is generated by the class of the projective bundle obtained by restricting the universal projective bundle. These results were proved earlier in [1] under the assumption that k = C . [ABSTRACT FROM AUTHOR]

Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω -rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate. [ABSTRACT FROM AUTHOR]

Let r ≥ 2 and r be even. An r -hypergraph G on n vertices is called odd-colorable if there exists a map φ : [ n ] → [ r ] such that for any edge { j 1 , j 2 , … , j r } of G , we have φ ( j 1 ) + φ ( j 2 ) + ⋅ ⋯ ⋅ + φ ( j r ) ≡ r ∕ 2 ( mod r ) . In this paper, we first determine that, if r = 2 q ( 2 t + 1 ) and n ≥ 2 q ( 2 q − 1 ) r , then the maximum chromatic number in the class of the odd-colorable r -hypergraphs on n vertices is 2 q , which answers a question raised by V. Nikiforov recently in Nikiforov (2017). We also study some applications of the spectral symmetry of the odd-colorable r -hypergraphs given in the same paper by V. Nikiforov. We show that the Laplacian spectrum S p e c ( L ( G ) ) and the signless Laplacian spectrum S p e c ( Q ( G ) ) of an r -hypergraph G are equal if and only if r is even and G is odd-colorable. As an application of this result, we give an affirmative answer for the remaining unsolved case r ⁄ ≡ 0 ( m o d 4 ) of a question raised in Shao et al. (2015) about whether S p e c ( L ( G ) ) = S p e c ( Q ( G ) ) implies that L ( G ) and Q ( G ) have the same H-spectrum. [ABSTRACT FROM AUTHOR]

In this paper we continue studying the independent transversal domination number in a graph, i.e., the cardinality of a smallest dominating set which intersects each maximum independent set. As our main result, we prove two upper bounds on the independent transversal domination number in terms of the order and minimum degree of a graph. [ABSTRACT FROM AUTHOR]

The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]

In this paper, we establish some scaling invariant regularity criteria for the Navier–Stokes–Maxwell system. [ABSTRACT FROM AUTHOR]

The optimal convergence rates on fast multipole methods (FMMs) for different Green’s functions are considered. Simpler convergence analysis and the more accurate convergence rates are presented. [ABSTRACT FROM AUTHOR]

In this paper, the homoclinic breather limit method is employed to find the breather wave and the rational rogue wave solutions of the ( 2 + 1 )-dimensional Ito equation. Moreover, based on its bilinear form, the solitary wave solutions of the equation are also presented with a detailed derivation. The dynamic behaviors of breather waves, rogue waves and solitary waves are analyzed with some graphics, respectively. The results imply that the extreme behavior of the breather solitary wave yields the rogue wave for the ( 2 + 1 )-dimensional Ito equation. [ABSTRACT FROM AUTHOR]

The focus of this work is on two new techniques for imposing maximum length scale in topology optimization. Restrictions on the maximum length scale provide designers with full control over the optimized structure and open possibilities to tailor the optimized design for broader range of manufacturing processes by fulfilling the associated technological constraints. One of the proposed methods is based on combination of several filters and builds on top of the classical density filtering which can be viewed as a low pass filter applied to the design parametrization. The main idea is to construct band pass filter which restricts the appearance of very thin and very thick elements in the design. In combination with the robust design optimization formulation the methodology results in manufacturable designs without the need of any post processing. The second technique provides more strict control on the maximum design features and is developed with the help of morphological operators. The formulation relies on a small number of additional constraints. Both approaches are demonstrated on optimization problems in linear elasticity. [ABSTRACT FROM AUTHOR]

Let C 2 be the group of order 2. We prove K 2 ( Z [ C 2 × C 2 ] ) is isomorphic to ( Z / 2 ) 6 and give an F 2 -basis of it. As an application, we show W h 2 ( C 2 × C 2 ) is isomorphic to ( Z / 2 ) 2 . [ABSTRACT FROM AUTHOR]

We present a new class of solvable systems of difference equations of interest by describing a method for finding its general solution. [ABSTRACT FROM AUTHOR]

The present paper shows that for a given integer k ≥ 2 it is possible to construct an at least k -differentiable Riemannian metric on the sphere of a certain dimension such that the cut locus of a point of it becomes a fractal. Moreover, we show that this construction can be extended to the case of Finslerian spheres as well. [ABSTRACT FROM AUTHOR]

A contact metric manifold is said to be H - contact , if its characteristic vector field is harmonic. We prove that the unit tangent bundle of a Riemannian manifold M equipped with the standard contact metric structure is H -contact if and only if M is 2-stein. [ABSTRACT FROM AUTHOR]

We show that the d -cube is determined by the spectrum of its distance matrix. [ABSTRACT FROM AUTHOR]

We obtain some conditions about the weighted shift and the composition operators on ℓ p to be ( m , q ) -isometries. In particular, we prove that if T is a strict ( 2 , q ) isometry, then p = q , whether T is a weighted shift or a composition operator on ℓ p . Moreover, we characterize the admissible weights for the weighted shift to be a strict ( 3 , p ) -isometry on ℓ p . The case of strict ( 4 , p ) -isometry is also studied. [ABSTRACT FROM AUTHOR]

In this paper we give a complete classification of all n -dimensional non-Lie Malcev algebras with ( n − 4 ) -dimensional annihilator over an algebraically closed field of characteristic 0. We also show that such algebras are special. [ABSTRACT FROM AUTHOR]

An edge-coloured connected graph G is rainbow connected if each two vertices are connected by a path whose edges have distinct colours. If such a colouring uses k colours then G is called k -rainbow connected. The rainbow connection number of G , denoted by rc ( G ) , is the minimum k such that G is k -rainbow connected. Even the problem to decide whether rc ( G ) = 2 is NP-complete. It has been shown that if G is a connected graph of order n and size m with n − 2 2 + 2 ≤ m ≤ n − 1 2 , then 2 ≤ rc ( G ) ≤ 3 . In this paper we will present sufficient conditions for graphs G of this size to fulfil rc ( G ) = 2 depending on vertex degrees. [ABSTRACT FROM AUTHOR]

Colour degree matrix problems, also known as edge-disjoint realisation and edge packing problems, have connections for example to discrete tomography. Necessary and sufficient conditions are known for a demand matrix to be the colour degree matrix of an edge-coloured forest. We give necessary and sufficient conditions for a demand matrix to be realisable by a graph with at most one cycle. [ABSTRACT FROM AUTHOR]

This paper investigates the structure of points u ∈ A N that are such that the omega-limit set ω ( u , σ ) is precisely X , where X ⊆ A N is an internally transitive shift space. We then use those results to study the possible structures of the omega-limit set of the turning point for a unimodal map. Examples are provided of unimodal maps f where no iterate of the turning point c is recurrent and ω ( c , f ) is either a minimal Cantor set or properly contains a minimal Cantor set. [ABSTRACT FROM AUTHOR]

In this note, we prove that a well-filtered dcpo L is coherent in its Scott topology if and only if for every x , y ∈ L , ↑ x ∩ ↑ y is compact in the Scott topology. We use this result to prove that a well-filtered dcpo L is Lawson-compact if and only if it is patch-compact if and only if L is finitely generated and ↑ x ∩ ↑ y is compact in the Scott topology for every x , y ∈ L . [ABSTRACT FROM AUTHOR]

In 2008, Liang-Xue Peng defined a weakening of the D -space property known as the transitively D property. He asked whether or not every transitively D -space is D . We show that three different examples of linearly Lindelöf, non-Lindelöf spaces are transitively D but not D , answering Peng's question in the negative. [ABSTRACT FROM AUTHOR]

Let M be a hyperbolizable, non-trivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of π 1 ( M ) into PSL ( 2 , C ) are separable-stable. The set of separable-stable representations forms a domain of discontinuity for the action of Out ( π 1 ( M ) ) on the PSL ( 2 , C ) -character variety of π 1 ( M ) . [ABSTRACT FROM AUTHOR]

We consider several generalized metric properties and study the relation between a space X satisfying such property and its n -fold symmetric product satisfying the same property. [ABSTRACT FROM AUTHOR]

Let E (respectively; T , S ) denote the set of all lines which are external (respectively; tangent, secant) to an irreducible conic in P G ( 2 , q ) . We give a brief survey of the known results regarding the minimum size L -blocking sets of P G ( 2 , q ) for L ∈ { E , S , T ∪ E , T ∪ S } and study the other two cases when L = T , E ∪ S . [ABSTRACT FROM AUTHOR]

We classify all compact simply connected biquotients of the form G ⫽ SU ( 2 ) 2 for G = SU ( 4 ) , SO ( 7 ) , Spin ( 7 ) , or G = G 2 × SU ( 2 ) . In particular, we show there are precisely 2 inhomogeneous reduced biquotients in the first and last case, and 10 in the middle cases. [ABSTRACT FROM AUTHOR]

We show that for every 2-bridge knot K , there is an infinite family of Montesinos knots { K q } such that each K q is 2-adjacent to K . We also give a new example of 2-adjacency relation between 2-bridge knots. [ABSTRACT FROM AUTHOR]

Spatial visualization is a crucial ability to understand and solve real world problems. Typically, important features of visual-spatial abilities in mathematics learning have been the skills required to construct mental models of mathematical objects from teacher drawings or oral descriptions. However, spatial ability is not a static trait but instead a dynamic process which could be fostered through interaction of real and virtual objects. This ability could be enriched with the development of new technologies such as augmented reality. We are part of a team of innovative and educational research aiming to foster mathematical cognitive skills, crucial but generally taken for granted. The purpose of this paper is to present an augmented reality application in order to promote spatial visualization in Calculus courses for engineering students. [ABSTRACT FROM AUTHOR]

Assuming AD + + V = L ( P ( R ) ) , and assuming there is no proper class inner model containing all the reals that satisfies AD R + “ θ is regular” , we prove that in some forcing extension, either V is a derived model of a premouse or V embeds into a derived model of a premouse. [ABSTRACT FROM AUTHOR]

Under the simple conditions on f and g , we show that entire positive k -convex radial solutions exist for the Hessian equation σ k ( λ ( D 2 u ) ) = p ( | x | ) f ( u ) , x ∈ R N and system σ k ( λ ( D 2 u ) ) = p ( | x | ) f ( v ) , σ k ( λ ( D 2 v ) ) = q ( | x | ) g ( u ) , x ∈ R N , where p , q : [ 0 , ∞ ) → ( 0 , ∞ ) are continuous. [ABSTRACT FROM AUTHOR]

We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal κ need not be weakly compact in HOD, and there can be a proper class of supercompact cardinals in V , none of them weakly compact in HOD, with no supercompact cardinals in HOD. Similar results hold for many other types of large cardinals, such as measurable and strong cardinals. [ABSTRACT FROM AUTHOR]

A consistent Riccati expansion (CRE) method is developed for a special Kuramoto–Sivashinsky (KS) equation and we prove the general KS equation is non-CRE solvable. Furthermore, we obtain the soliton–cnoidal wave interaction solution of the special KS equation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Z -eigenpair of a tensor, in particular, an irreducible nonnegative tensor. We present some bounds for the eigenvector and Z -spectral radius. The proposed bounds improve some existing ones. An example with practical applications is given to show the proposed bound. [ABSTRACT FROM AUTHOR]

In this paper, we define the sign pattern tenors, minimum (maximum) rank of sign pattern tenors, term rank of tensors and sign nonsingular tensors. The necessity and sufficiency for the minimum rank of sign pattern tenors to be 1 is given. We show that the maximum rank of a sign pattern tensor is not less than the term rank and the minimum rank of the sign pattern of a sign nonsingular tensor is not less than its dimension. We get some characterizations of tensors having sign left or sign right inverses. [ABSTRACT FROM AUTHOR]

Let V be a nonsingular quadratic space over a field K of characteristic 2. We show that if n > 4 , then every element π in the special orthogonal group SO ( V ) is a product of an even number of half turns. If dim ⁡ B ( π ) = 2 k , then the length of π with respect to the half turns is k , k + 1 or k + 2 . [ABSTRACT FROM AUTHOR]

In this paper a novel HNSI (Handwritten Numeral Script Identification) framework to identify scripts from document images containing numeral text written by any one of the four popular Indic scripts namely Bangla, Devanagari, Roman and Urdu has been proposed. A dataset of 4000 word-level numeral images with equal distribution of each script type are collected from different individuals with varying age, sex and educational qualification. Some spatial and frequency domain features has been computed and a 55-dimensional feature vector is developed. During experimentation the whole dataset is divided into 2:1 ratio for training and testing. Performance of different classifiers is compared and MLP is found to be the best one while evaluating accuracy rate for combinations like Four-scripts, Tri-scripts and Bi-scripts. [ABSTRACT FROM AUTHOR]

Hedayat et al. first introduced balanced sampling plans for the exclusion of contiguous units. Wright detailed the results of a preliminary investigation of two-dimensional balanced sampling plans avoiding adjacent units (2-BSAs), and pointed out explicitly three types of 2-BSAs, which have different adjacency scheme, namely “Row and Column”, “Sharing a Border” and “Island”. This paper will provide more details for the three types of 2-BSAs from the point of view of design theory. [ABSTRACT FROM AUTHOR]

The main purpose of the paper is the proof of a cardinal inequality for a space with points G δ , obtained with the help of a long version of the Menger game. This result improves a similar one of Scheepers and Tall. [ABSTRACT FROM AUTHOR]

A graph G is said to be determined by its generalized spectrum (DGS for short) if for any graph H , H and G are cospectral with cospectral complements implies that H is isomorphic to G . Let G ˆ be the graph obtained from G by adding a pendent edge at every vertex of G . We show that G ˆ is DGS if and only if G is DGS for some graph G . This gives a simple way to construct large DGS graphs from small ones explicitly. In particular, we show that every graph in the infinite sequence G , G ˆ , G ˆ ˆ , ⋯ is DGS, for some DGS graph G . [ABSTRACT FROM AUTHOR]

Let G be a connected graph of order n and let D = D ( G ) be its distance matrix. Suppose that λ 1 ( D ) ≥ ⋯ ≥ λ n ( D ) are the eigenvalues of D ( G ) . Then DE ( G ) = ∑ i = 1 n | λ i ( D ( G ) ) | is called the distance energy of G . In this paper, we characterize all connected graphs with DE ( G ) ∈ [ 2 n − 2 , 2 n ] . [ABSTRACT FROM AUTHOR]

This is a survey or exposition of a particular collection of results and open problems involving snarks — simple “cubic” (3-valent) graphs for which, for nontrivial reasons, the edges cannot be 3-colored. The results and problems here are rooted in a series of papers by László Kászonyi that were published in the early 1970s. The problems posed in this survey paper can be tackled without too much specialized mathematical preparation, and in particular seem well suited for interested undergraduate mathematics students to pursue as independent research projects. This survey paper is intended to facilitate research on these problems. [ABSTRACT FROM AUTHOR]

For a topological space X , let Σ ( X ) be the family of all subrings of C ( X ) containing C ⁎ ( X ) . In 1997, S.K. Acharyya, K.C. Chattopadhyay and D.P. Ghosh showed that for an A ( X ) ∈ Σ ( X ) , the intersection of all free maximal ideals of A ( X ) is an ideal of C ∞ ( X ) containing C K ( X ) . In this paper we define z ∞ -ideals and nicely balanced ideals of C ∞ ( X ) and show that if I is a z ∞ -ideal of C ∞ ( X ) then I is the intersection of all free maximal ideals of A ( X ) for some A ( X ) ∈ Σ ( X ) if and only if I is nicely balanced. Examples related to z ∞ -ideals and nicely balanced ideals are given. [ABSTRACT FROM AUTHOR]

The classical first and second Zagreb indices of a graph G are defined as M 1 = ∑ v d v 2 and M 2 = ∑ u v d u d v , where d v is the degree of the vertex v of G . So far, the difference of M 1 and M 2 has not been studied. We show that this difference is closely related to the vertex-degree-based invariant R M 2 = ∑ u v ( d u − 1 ) ( d v − 1 ) , and determine a few basic properties of R M 2 . [ABSTRACT FROM AUTHOR]