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The primary aim of this paper is to investigate the asymptotic distribution of the zeros of certain classes of hypergeometric $ {}_{q+1}F_{q} $ q + 1 F q polynomials. We employ classical analytical techniques, including Watson's lemma and the method of steepest descent, to understand the asymptotic behavior of these polynomials: $$\begin{align*} & _{q+1}F_{q}\left(-n,kn+\alpha,\ldots, kn+\alpha+\frac{q-1}{q};kn+\beta,\ldots,kn+\beta+\frac{q-1}{q};z\right)\\ &\quad (n\rightarrow \infty), \end{align*} $$ q + 1 F q (− n , kn + α , ... , kn + α + q − 1 q ; kn + β , ... , kn + β + q − 1 q ; z) (n → ∞) , where n is a nonnegative integer, q is a positive integer and the constant parameters α and β are constrained by $ \alpha { α < β. By applying the general results established in this paper, we generate numerical evidence and graphical illustrations using Mathematica to show the clustering of zeros on certain curves. [ABSTRACT FROM AUTHOR]

Our goal of this paper is to find a construction of all ℓ-quasi-cyclic self-dual codes over a finite field $ {\mathbb F}_q $ F q of length $ m\ell $ mℓ for every positive even integer ℓ. In this paper, we study the case where $ x^m-1 $ x m − 1 has an arbitrary number of irreducible factors in $ {\mathbb F}_q [x] $ F q [ x ] ; in the previous studies, only some special cases where $ x^m-1 $ x m − 1 has exactly two or three irreducible factors in $ {\mathbb F}_q [x] $ F q [ x ] , were studied. Firstly, the binary code case is completed: for any even positive integer ℓ, every binary ℓ-quasi-cyclic self-dual code can be obtained by our construction. Secondly, we work on the q-ary code cases for an odd prime power q. We find an explicit method for construction of all ℓ-quasi-cyclic self-dual codes over $ {\mathbb F}_q $ F q of length $ m\ell $ mℓ for any even positive integer ℓ, where we require that $ q \equiv 1 \pmod {4} $ q ≡ 1 (mod 4) if the index $ \ell \ge 6 $ ℓ ≥ 6. By implementation of our method, we obtain a new optimal binary self-dual code $ [172, 86, 24] $ [ 172 , 86 , 24 ] , which is also a quasi-cyclic code of index 4. [ABSTRACT FROM AUTHOR]

AbstractIn 2021, we introduced one type of the generalization of dominator coloring via packing coloring and distance domination. In this paper, we present a second type of such generalization, namely distance dominator packing coloring of type II, defined as follows. A coloring c is a k-distance dominator packing coloring of type II of G if it is a k-packing coloring of G and for each u ∈ V (G) there exists i ∈ {1, 2, 3, . . . , k} such that u c(u)-distance dominates each vertex from the color class of color i (i.e., the distance between u and all vertices from color class of color i is at most c(u)). The smallest integer k such that there exists a k-distance dominator packing coloring of G is the distance dominator packing chromatic number of type II of G, denoted by . In this paper, we provide some lower and upper bounds on the distance dominator packing chromatic number of type II, characterize connected graphs G with , and consider the relation between the packing coloring, distance dominator packing coloring of type I (introduced by Ferme and Mesarič Štesl in 2021) and distance dominator packing coloring of type II for a given graph. [ABSTRACT FROM AUTHOR]

Let m, n be integers such that 1

The presence of turning points (stationary points like maxima and minima) in the Parameter-versus-state map (PSM) curve of a memristor can be beneficial in several memristive uses like multi-level logic design, multi-bit memories, and chaos generation circuits. Surprisingly the memristors with these types of PSM curves exhibit multiple crossing points in the transient input v-i contours. In this paper, the memductance model has been derived for such non-linear memristors exhibiting multi-cross-over characteristics. In the presented framework, the coefficients-related condition for the multi-turning point PSM curve has been derived, a necessary condition for the multi-crossing v-i contour. The condition related to the memristor operating parameters has also been reported taking both input signal and initial states into consideration. To realise the derived memductance model corresponding to the three cross-over memristive behaviour, an OTA-based memristor emulator has been developed. Unlike some existing fractional order non-symmetric multi-crossing memristor emulators, the proposed emulator circuit realises an integer order memristor function operating at moderate frequencies. The realised emulator uses only four OTAs and three grounded passive circuit elements with no external multiplier. For the CMOS implementation of employed OTA, the simulation results are obtained to verify the three pinch-off behaviour. [ABSTRACT FROM AUTHOR]

The fault tolerability of the network is usually measured by the classical or generalized connectivity of the graph. For any subset $ S \subseteq V\left (G \right) $ S ⊆ V (G) with $ \left | S \right | \ge 2 $ | S | ≥ 2 , a tree T is called an S-tree if $ S \subseteq V\left (T \right) $ S ⊆ V (T) . Furthermore, any two S-tree $ T_1 $ T 1 and $ T_2 $ T 2 are internally disjoint if $ E\left ({{T_1}} \right) \cap E\left ({{T_2}} \right) = \emptyset $ E ( T 1 ) ∩ E ( T 2 ) = ∅ and $ V\left ({{T_1}} \right) \cap V\left ({{T_2}} \right) = S $ V ( T 1 ) ∩ V ( T 2 ) = S. We denote by $ {\kappa _G}\left (S \right) $ κ G (S) the maximum number of pairwise internally disjoint S-trees in G. For an integer $ k \ge 2 $ k ≥ 2 , the generalized k-connectivity of a graph G is defined as $ {\kappa _k}\left (G \right) = \min \left \{ {{\kappa _G}\left (S \right) | S \subseteq V\left (G \right)} \right. $ κ k (G) = min { κ G (S) | S ⊆ V (G) and $ \left. {\left | S \right | = k} \right \} $ | S | = k } . In this paper, we establish the generalized 4-connectivity of the Cayley graph $ CT_n $ C T n generated by complete graphs. [ABSTRACT FROM AUTHOR]

The weight of a partition is the sum of its nonzero coordinates. Let R and S be partitions of the same weight and $ {\mathcal {A}}(R,S) $ A (R , S) be the class of all $ (0,1) $ (0 , 1) -matrices with row sums R and column sums S. For a positive integer t, the t-term rank of a matrix $ A\in {\mathcal {A}}(R,S) $ A ∈ A (R , S) , denoted $ \rho _t(A) $ ρ t (A) , is defined as the largest number of 1's in A with at most one 1 in each column and at most t 1's in each row. The term rank partition of A is the partition $$\begin{align*} term\ \rho(A) & :=(\rho_1(A)-\rho_0(A),\rho_2(A) \\ & \quad - \rho_1(A),\ldots ,\rho_t(A)-\rho_{t-1}(A),\ldots), \end{align*} $$ term ρ (A) := (ρ 1 (A) − ρ 0 (A) , ρ 2 (A) − ρ 1 (A) , ... , ρ t (A) − ρ t − 1 (A) , ...) , where $ \rho _0(A)=0 $ ρ 0 (A) = 0. Let θ be a partition of weight equal to the number of nonzero coordinates of S. In this paper, we study conditions for the existence of a matrix $ C\in {\mathcal {A}}(R,S) $ C ∈ A (R , S) with $ term\ \rho (C)=\theta. $ term ρ (C) = θ. [ABSTRACT FROM AUTHOR]

Let v, k, t be positive integers and let $ G(v,k,t) $ G (v , k , t) be the uniform subset graph, defined by all k-subsets of a v-set as its vertices with edges connecting all k-subsets intersecting exactly at t elements. In this paper, we give non-trivial dominating sets for $ G(v,k,2) $ G (v , k , 2) -graphs and their complements for k = 3, 4, 5, 6. The given domination numbers of some of these graphs are sharper than the known bounds. [ABSTRACT FROM AUTHOR]

Let $ n\geqslant 2 $ n ⩾ 2 be an integer and let $ T_n({\mathbb {D}}) $ T n (D) be the ring of $ n\times n $ n × n upper triangular matrices over a division ring $ {\mathbb {D}} $ D with centre $ Z(T_n({\mathbb {D}})) $ Z (T n (D)). In this paper, we characterize additive maps $ \psi :T_n({\mathbb {D}})\rightarrow T_n({\mathbb {D}}) $ ψ : T n (D) → T n (D) satisfying $ [\psi (A),\psi (B)]-[A,B]\in Z(T_n({\mathbb {D}})) $ [ ψ (A) , ψ (B) ] − [ A , B ] ∈ Z (T n (D)) for all $ A,B\in T_n({\mathbb {D}}) $ A , B ∈ T n (D). We then deduce from this result a complete characterization of strong commutativity preserving additive maps $ \psi :T_n({\mathbb {D}})\rightarrow T_n({\mathbb {D}}) $ ψ : T n (D) → T n (D) on rank k upper triangular matrices, where $ 1\leqslant k\leqslant n $ 1 ⩽ k ⩽ n is a fixed integer such that $ k\neq n $ k ≠ n when $ |{\mathbb {D}}|=2 $ | D | = 2. [ABSTRACT FROM AUTHOR]

This paper deals with the Generalised Workforce Scheduling and Routing Problem (GWSRP) where 9 temporal constraints ensuring visit dependencies are all together taken into account and where customer and worker's quality of service are taken into consideration. A Constraint-Programming based Decomposition Method (CPDM) is proposed, firstly based on a relaxation of coordination constraints and a column generation, and secondly with an iterative insertion of coordination constraint by constraint programming solver. Numerical experiments are achieved on huge instances derived from WSRP benchmark instances with up to 177 customers, 59 vehicles and coordination constraints. The CPDM is able to find nearly optimal solution for medium-size instances and find high-quality solution for huge-size instances whereas CPLEX solver applied to a mixed integer linear model is not able to give a solution in this case. [ABSTRACT FROM AUTHOR]

In this paper, loss due to staggered-via in SIW (Substrate Integrated Waveguide) is analyzed with the help of S-parameter responses and field diagrams. It is observed that staggered-via improves the response of an SIW structure, with higher via pitch (w) to via diameter (d) ratio (w/d), but the loss increases drastically at certain discrete frequencies for which λ / 2 n equals to w, where λ is the guided wavelength corresponding to the frequency and n is any integer value excluding zero. This study will be helpful in choosing between the use of single row of vias or staggered-vias as a sidewall, while designing SIWs at higher frequencies, where it is difficult to use conventional w/d ratio values. [ABSTRACT FROM AUTHOR]

Let p 1 < p 2 < ⋯ < p n be positive numbers, then for any integer m the Loewner matrix associated with the function x m is given by L m = (p i m − p j m) / (p i − p j) i , j = 1 n. A question was left open in a paper [Bhatia R, Friedland S, Jain T. Inertia of loewner matrices. Indiana Univ Math J. 2016;65:1251–1261] by Bhatia, Friedland and Jain to find formulas for the determinants of the matrices L m in the case n = 3. We aim to answer this question firmly in terms of the Schur polynomials in this paper. [ABSTRACT FROM AUTHOR]

RSA is a well-known cryptosystem in Modern Cryptography and its efficiency is based on the hardness of the Integer Factorization problem. The algorithm is shown to be vulnerable to several attacks in a number of special scenarios with assumptions. In this paper, the strength of RSA is investigated if the primes in the modulus are close and the same modulus is used for two instances. The attack is highly efficient compared to other known attacks which are only concentrated on either closeness of the primes or the same modulus used for two or more instances. This attack examines the closeness of the primes chosen whenever the RSA system is used for two instances with the same modulus. The LLL algorithm is used to obtain the bound, and the bound is highly efficient compared to other known attacks. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Choquard equations with a local perturbation − Δ u + u = ∫ R N | u (y) | 2 | x − y | N − α d y u + | u | q − 2 u in R N , where N ≥ 3 , α ∈ ((N − 4) + , N) , q ∈ (2 , 2 N / (N − 2)). By using variational method and approximating approach, we prove that for any given positive integer k, the above equation has a least energy radial solution changing sign exactly k times. This solution is constructed as the limit of such solutions for the following Choquard equations − Δ u + u = ∫ R N | u (y) | p | x − y | N − α d y | u | p − 2 u + | u | q − 2 u in R N , as p ↘ 2 + . Our result improves and extends the previous results in the literature. [ABSTRACT FROM AUTHOR]

Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward descriptions in terms of how often each value in the sequence occurs. In this paper, we generalize the most classical examples to a larger family of sequences parametrized by linear recurrence relations. Each of our sequences can be constructed in three different ways: via a nested recurrence relation, from labeled infinite trees, or by using Zeckendorf-like strings of digits to describe its frequency sequence. We conclude the paper by discussing the asymptotic behaviors of our sequences. [ABSTRACT FROM AUTHOR]

AbstractLet k be an arbitrary field and let b>1,n>1 and a be three positive integers. In this paper we explicitly describe a minimal S-graded free resolution of the semigroup algebra k[S] when S is a generalized repunit numerical semigroup, that is, when S is the submonoid of N generated by {a1,a2,…,an} where a1=∑j=0n−1bj and ai−ai−1=a bi−2, i=2,…,n, with gcd(a,a1)=1. [ABSTRACT FROM AUTHOR]

AbstractLet m, n be integers with m>n . Denote Mm,n by the set of all m×n matrices over the field F of characteristic zero. Let I be an n×m matrix with (i,i) -position 1 for any 1≤i≤n , and 0 in other position. Define a bracket [A,B]=AIB−BIA , where A,B∈Mm,n . Then Mm,n with this bracket is a Lie algebra, called non-square linear Lie algebra, denoted by gl(m×n,F) . In this paper, all derivations and biderivations of gl(m×n,F) are determined. As applications of biderivations, the linear commuting maps and commutative post-Lie algebra structures on gl(m×n,F) are given. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we consider a class of nonlinear p-k-Hessian systems with the gradient termwhere γ > 0, p > 1, and 1 ≤ k ≤ N is an integer. We show some existence, boundedness and blow-up results of the entire positive p-k-convex radial solutions based on the monotone iterative method. Finally, we present an example to illustrate our result. [ABSTRACT FROM AUTHOR]

Given a finite group G, denote by cs(G) the set of the sizes of the conjugacy classes of G and by Cent(G) the set of the centralizers of elements of G. Consider a prime p and integers s ≥ 2 and n ≥ 2 , with gcd (p , s) = 1 . In this paper, some relations between cs(G) and | Cent (G) | are established in the case where cs (G) = { 1 , p n , p n − 1 s } . Further, when p ∈ { 2 , 3 } , we determine the values of s and the structure of a finite group G such that cs (G) = { 1 , p n , p n − 1 s } . We also describe the structure of an AC-group G such that [ G : Z (G) ] = 3 n s and | Cent (G) | = 1 + ∑ i = 0 n 3 i , where gcd (3 , s) = 1 . [ABSTRACT FROM AUTHOR]

AbstractLet D be an integral domain and D[​[x]​] be the power series ring over D. In this paper, we study the primality of x−α in D[​[x]​], where α∈D. For this purpose, we generalize the definition of a prime element as follows. For a positive integer N, a nonzero nonunit α∈D is called an N-prime element if for any a,b∈D, αN|ab implies α|a or α|b. We prove that if α is an N-prime element for some N, then x−α is a prime element in D[​[x]​]. Surprisingly, it is shown that the converse also holds when D is a PID, a valuation domain, or a Dedekind domain. In other words, when D is a PID, a valuation domain, or a Dedekind domain, a necessary and sufficient condition for x−α to be a prime element in D[​[x]​] is α is an N-prime element in D for some N. This however does not hold for other types of integral domains such as UFDs or Krull domains. We also investigate the N-prime property in an arbitrary integral domain and give other (equivalent) conditions for an element α in the aforementioned types of integral domains to be an N-prime element. [ABSTRACT FROM AUTHOR]

AbstractLet R be a commutative noetherian ring and a an ideal of R. The goal of this paper is to establish the local-global principle for the artinianness dimension ra(M), where ra(M) is the smallest integer such that the local homology module of M is not artinian. For an artinian R-module M with the set CoassRHra(M)a(M) finite, we show that ra(M)=inf{raRp(HomR(Rp,M))|p∈SpecR}. And the class of all modules N such that CoassRN is finite is studied. [ABSTRACT FROM AUTHOR]

In the present paper we shall obtain the following result: Let n ≥ 2 and m ≥ 1 be integers. Let p (x 1 , ... , x m) be a polynomial with zero constant term in non-commutative variables over an algebraically closed field K. Suppose that 1 ≤ r ≤ n − 1 , where r is the order of p. Then p (T n (K)) is a dense subset of T n (K) (r − 1) (with respect to the Zariski topology). This is a solution of a problem presented by Gargate and de Mello and a supplement to a result obtained by Panja and Prasad in 2023. [ABSTRACT FROM AUTHOR]

We study the rings Nil D of nilpotent elements of R-derivations D on polynomial rings over a UFD R containing Q . The main result of this paper determines Nil D of the monomial derivations D on R [ x , y ] . Furthermore, as its application, we prove that, for each positive integer m, there exists a monomial R-derivation with a slice on R [ x , y , z ] such that the minimal number of generators of its kernel equals m. [ABSTRACT FROM AUTHOR]

A large number of problems in a distribution supply chain require that decisions are made in the presence of the bullwhip effect phenomenon. The impact of the order batching policies on the bullwhip effect is analysed in this paper, when cycle demand on a multi-echelon supply chain operating is considered. While investigating which bullwhip effect metrics are more adequate to measure the bullwhip effect in these type of systems, the optimal reordering plan that minimises the operation costs of the overall system is calculated. A Mixed Integer Linear Programming (MILP) model is developed that takes into account an inventory and distribution system formed by multiple warehouses and retailers with lateral transshipments. The bullwhip effect is measured through four metrics: the echelon average inventory; the echelon inventory variance ratio; the echelon average order; and the echelon order rate variance ratio. As conclusion the inventory metrics suggest that (i) using batching policy reduces instability; (ii) batching may reduce in general order variance if using larger batches and (iii) cycle demand length has no major impact in the bullwhip effect. A motivational example and a real word case study are used and tested. [ABSTRACT FROM AUTHOR]

A partial disassembly line balancing problem under uncertainty is studied in this paper, which concerns the allocation of a sequence of tasks to workstations such that the overall profit is maximised. We consider the processing time uncertainty and develop robust solutions to accommodate it. The problem is formulated as a non-linear robust integer program, which is then converted into an equivalent linear program. Due to the intractability of such problems, the exact algorithms are only applicable to small-scale instances. We develop an improved migrating birds optimisation algorithm. Two enhancement techniques are proposed. The first one finds the optimal number of tasks to be performed for each sequence rather than random selection used in the literature; while the second one exploits the specific problem structure to construct effective neighbourhoods. The numerical results show the strong performance of our proposal compared to CPLEX and the improved gravitational search algorithm (IGSA), especially for large-scale problems. Moreover, the enhancement due to the proposed techniques is obvious across all instances considered. [ABSTRACT FROM AUTHOR]

Let R be an associative ring and let s ≥ 1 be a fixed integer. An additive map h on R is called a homoderivation if h (x y) = h (x) h (y) + h (x) y + x h (y) holds for all x , y ∈ R. In 1978, Herstein proved that a prime ring R of char (R) ≠ 2 is commutative if there is a nonzero derivation d of R such that [ d (x) , d (y) ] = 0 for all x , y ∈ R . The main objective of this paper is to prove the above mentioned result for homoderivations with nilpotency 's' in prime rings. Moreover, we prove that if a prime ring admits homoderivations h1 and h2 such that h 1 ° h 2 = h 2 ° h 1 and h 1 s 1 ° h 2 s 2 = 0 for positive integers s1 and s2, then at least one of the homoderivations must be nilpotent. [ABSTRACT FROM AUTHOR]

Let K be a field, [ n ] = { 1 , ... , n } and H = ([ n ] , E) be a hypergraph. For an integer d ≥ 1 the Lovász-Saks-Schrijver ideal (LSS-ideal) L H K (d) ⊆ K [ y i j : (i , j) ∈ [ n ] × [ d ] ] is the ideal generated by the polynomials f e (d) = ∑ j = 1 d ∏ i ∈ e y i j for edges e of H. In this paper for an algebraically closed field K and a k-uniform hypergraph H = ([ n ] , E) we employ a connection between LSS-ideals and coordinate sections of the closure of the set S n , k d of homogeneous degree k symmetric tensors in n variables of rank ≤ d to derive results on the irreducibility of its coordinate sections. To this end we provide results on primality and the complete intersection property of L H K (d) . We then use the combinatorial concept of positive matching decomposition of a hypergraph H to provide bounds on when L H K (d) turns prime to provide results on the irreducibility of coordinate sections of S n , k d . [ABSTRACT FROM AUTHOR]

Let m be a positive integer such that p ∤ m where p is prime. In this paper we find the number of conjugacy classes of completely reducible cyclic subgroups in GL (2 , q) of order m, where q is a power of p. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (A , m) -partial isometry for a positive operator A and a nonnegative integer m. This family of operators contains both the class of (A , m) -isometries discussed in Sid Ahmed and Saddi [A-m-isometric operators in semi-Hilbertian spaces. Linear Algebra Appl. 2012;436:3930–3942] and that of m-partial isometries introduced in Saddi and Sid Ahmed [m-partial isometries on Hilbert spaces. Int J Funct Anal Oper Theory Appl. 2010;2(1):67–83]. First, we give some interesting algebraic properties of (A , m) -partial isometries, then we discuss a necessary and sufficient condition for an (A , m) -partial isometry to be an (A , m) -isometry. Finally, we give some spectral properties of (A , m) -partial isometries. [ABSTRACT FROM AUTHOR]

A restricted dth power of an ideal I is obtained by restricting the exponent vectors allowed to appear on the "natural" generating set of Id, for some integer d. In this paper, we study homological properties of restricted powers of complete intersections. We construct a generalization of the L-complex construction of Buchsbaum and Eisenbud. We use this resolution to compute an explicit basis for the Koszul homology which allows us to deduce that the quotient defined by any restricted dth power of a complete intersection is Golod, and construct an algebra structure on this complex. [ABSTRACT FROM AUTHOR]

Let S be a groupoid (magma) with zero 0, and let R = ⊕ s ∈ S R s be a contracted S-graded ring, that is, an S-graded ring with R 0 = 0. By G (H R) we denote the undirected power graph of a multiplicative subsemigroup H R = ∪ s ∈ S R s of R, and by G * (H R) a graph obtained from G (H R) by removing 0 and its incident edges. If Re is a nonzero ring component of R, then G * (R e) denotes a subgraph of G * (H R) , induced by R e *. In this paper we address a problem raised in [Abawajy, J., Kelarev, A., Chowdhury, M.: Power Graphs: A Survey. Electron. J. Graph Theory Appl. 1(2), 125–147 (2013)]. Namely, let S be torsion-free, that is, s n = t n implies s = t for all s, t ∈ S , and all positive integers n, and let S be 0-cancellative, that is, for all s, t, u ∈ S , su = tu ≠ 0 implies s = t , and us = ut ≠ 0 implies s = t. Also, let R be semisimple Artinian. We prove that if G * (R e) is connected for every nonzero ring component Re of R, then the connected components of G * (H R) are precisely the graphs G * (R e). [ABSTRACT FROM AUTHOR]

Let S V (z) be a class of Schrödinger-Virasoro type Lie algebras, where z ∈ Z . In this paper, we show that S V (z) is 2-local complete (namely, every 2-local derivation is a derivation) for almost all integers z's. We also introduce the notion of full diamond thin Lie algebras, and construct an example F from S V (− 1) . We completely determine the derivations of F by combinatoric techniques, and show that F is not 2-local complete. [ABSTRACT FROM AUTHOR]

In this paper we develop new identities for Euler sums with rational argument. We shall investigate and report on new Euler identities of weight for m,p,q positive integers and m + p + q an even integer, but with a non-unitary argument of the harmonic numbers. Some examples of these Euler identities will be given in terms of Riemann zeta values, Dirichlet values and other special functions. We shall also give an explicit solution to an integral with a log polylog integrand. [ABSTRACT FROM AUTHOR]

For a fixed integer n≥2, let Mn be the algebra of all n × n matrices over the complex field C. Let x1,x2∈Cn be two fixed nonzero vectors, and fix also y1,y2∈Cn. In this paper, we characterize linear bijective maps φ:Mn→Mn having the property that φ(A)φ(B)x2=y2 whenever ABx1=y1. [ABSTRACT FROM AUTHOR]

This paper proposes two integer linear programming formulations to solve the optimal stratification problem (OSP). In this problem, once given the number of strata and the total sample size, the cutoff points and sample allocation should be determined jointly to minimize an expression of variance and to solve the OSP corresponding to an integer nonlinear optimization problem. One proposed formulation determines the optimal cutoff points considering classical allocation methods from the literature, and a second formulation produces the global optimum regarding the determination of the cutoff points and the sample allocation to the strata. Both formulations were implemented using Gurobi solver and applied to a set of 20 datasets from the literature, with population sizes ranging from 91 to 16,057, considering six different scenarios concerning the number of strata and sample sizes. The results obtained indicate that the formulations are a good alternative for the resolution of the OSP. [ABSTRACT FROM AUTHOR]

Let ßA (ℍ) denote the algebra of bounded linear operators on a complex Hilbert space ℍ that admit A-adjoint operators, where A is a non-zero positive semi-definite operator on ℍ. A commuting operator tuple T = (T1 ,..., Td) ∈ ßA(ℍ)d is called jointly A-normaloid if rA(T) = ∥T∥A, where rA(T) and ∥T∥A represent the joint A-spectral radius and the joint operator A-seminorm of T, respectively. This paper aims to investigate this new class of operators and provides several examples. Furthermore, a characterization of A-normaloidity is established. Additionally, the joint Euclidean A-seminorm of a d-tuple of A-bounded operators T, denoted by , is examined. Specifically, for all positive integers n, we prove that the following equivalence holds for any commuting operator tuple. Here. Finally, several related questions are explored. [ABSTRACT FROM AUTHOR]

In the urban canyon environment, the integer ambiguity is hard to be fixed completely mainly because of the multipath effects, hence partial ambiguity resolution (PAR) is developed. This paper systematically introduces a new model-driven PAR method considering elevation and C/N0. Firstly, the theory of partial ambiguity resolution, the elevation-C/N0 function, and the proposed elevation-C/N0 PAR method are deduced in detail. Secondly, the proposed elevation-C/N0 method is applied in the static and dynamic experiments. The performances of the proposed method are compared with the full ambiguity resolution method, traditional elevation-dependent method, and C/N0-dependent method. Comparisons indicate that the proposed elevation-C/N0 method outperforms other methods. The results show that no matter in the urban static experiment or the dynamic experiment, the ambiguity resolution and positioning solutions can be improved. [ABSTRACT FROM AUTHOR]

Let D be an integral domain with quotient field K, X be an indeterminate over D, K [ X ] be the polynomial ring over K, n ≥ 2 be an integer, K [ θ ] = K [ X ] / (X n) , where θ = X + (X n) , and R n = D + θ K [ θ ] , i.e, R n = { f + (X n) ∈ K [ X ] / (X n) | f (0) ∈ D } . Then Rn is a subring of K [ θ ] with total quotient ring K [ θ ] . In this paper, we study several ring-theoretic properties of Rn, with a focus on Prüfer rings and Prüfer v-multiplication rings (PvMRs). For example, we show when Rn is a Prüfer ring, a Bézout ring, a PvMR, or a GCD ring. [ABSTRACT FROM AUTHOR]

In this paper, we present several explicit formulas for Appell polynomials in terms of the weighted Stirling numbers of the second kind. We also provide a unified approach to obtain a three-term recurrence formula for the computation of Appell polynomials. Several examples are given to illustrate our results. As an application, we define and study a new class of polynomials that we call SPI polynomials. They are related to sums of powers of integers. [ABSTRACT FROM AUTHOR]

Restoration of damaged highway-bridge networks is critical to the recovery of the networks' functionality in support of post-disaster recovery actions. Restoration-scheduling problems have traditionally assumed that parallel restoration actions to different bridges on a highway segment can be undertaken simultaneously. However, such assumption may have unfavorable consequences insofar as, in real-world scenarios, downtime may result from impassability of a segment due to blockage arising from the preceding restoration actions to their subsequent ones on the same segment. Consequently, downtime due to interactions of parallel restoration actions may hinder effective recovery of networks' functionality. Accordingly, this paper proposes an integer program to investigate the restoration interactions in post-earthquake highway–bridge networks and such interactions' impacts on optimal restoration scheduling and networks' resilience recovery processes. A hybrid genetic algorithm that combines a genetic algorithm with a specifically designed heuristic approach is developed to improve the proposed integer program's computational efficiency. The results of a case study using the proposed method and data from the 2008 Wenchuan Earthquake show that the downtime due to restoration interactions can delay the recovery of the networks' functionality, and thus that neglecting such interactions can lead to the overestimation of the networks' resilience. [ABSTRACT FROM AUTHOR]

For a character χ of a finite group G, the number cod (χ) = [ G : ker χ ] χ (1) is called the co-degree of χ. Let n ≥ 2 be an integer and Irr (G | Fit (G)) denote the set of irreducible characters whose kernels do not contain Fit (G) . In this paper, we show that if G is solvable and p n + 1 ∤ cod (χ) for every prime divisor p of | G | and every χ ∈ Irr (G | Fit (G)) , then the derived length of G is at most 2 log 2 (n) + log 2 (n − 1) + 4 . Then, we classify the finite non-solvable groups with non-trivial Fitting subgroups such that the co-degrees of their irreducible characters whose kernels do not contain the Fitting subgroups are cube-free. [ABSTRACT FROM AUTHOR]

Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The component connectivity is an important parameter for the reliability evaluation of interconnection networks and is a generalization of the traditional connectivity. Let g ≥ 0 be an integer and G be a connected graph. A g-component cut of G is a vertex set S such that G−S has at least g components. The g-component connectivity c κ g (G) of G is the size of the smallest g-component cut. Determining the g-component connectivity is still an unsolved problem in many interconnection networks. In this paper, we prove the lower bound of the g-component connectivity of any n-dimensional hypercube-like networks. We also determine the g-component connectivity of varietal hypercubes and crossed cubes which are the members of hypercube-like networks. As a by-product, we characterize the optimal g-component cut under the condition that any two vertices have exactly two common neighbors if they have of any n-dimensional hypercube-like networks. [ABSTRACT FROM AUTHOR]

The k-Fibonacci sequence { F n (k) } n starts with the values 0 , ... , 0 , 1 (a total of k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all integers c having at least two representations as a difference between a k-Fibonacci number and a Pell number. This paper continues and extends the previous work of [J.J. Bravo, C.A. Gómez, and J.L. Herrera, On the intersection of k-Fibonacci and Pell numbers, Bull. Korean Math. Soc. 56(2) (2019), pp. 535–547; S. Hernández, F. Luca, and L.M. Rivera, On Pillai's problem with the Fibonacci and Pell sequences, Soc. Mat. Mex. 25 (2019), pp. 495–507 and M.O. Hernane, F. Luca, S.E. Rihane, and A. Togbé, On Pillai's problem with Pell numbers and powers of 2, Hardy- Ramanujan J. 41 (2018), pp. 22–31]. [ABSTRACT FROM AUTHOR]

In this paper, the extended Resource Renting Problem (RRP/extended) is presented. The RRP/extended is a time-constrained project scheduling problem, in which the total project cost is minimised. In the RRP/extended, this total project cost is determined by a number of extra costs, which are defined in this paper. These costs are based on the costs that are used in the traditional Resource Renting Problem and the Total Adjustment Cost Problem. Therefore, the RRP/extended represents a union of these two problems. To solve the RRP/extended, a scatter search is developed. The building blocks of this scatter search are specifically designed for the RRP/extended. We introduce two crossovers and an improvement method. The efficiency of these building blocks will be shown in the paper. Furthermore, a sensitivity analysis is presented in which the five costs have diverse values. [ABSTRACT FROM AUTHOR]

Let m, n and p be integers with 3 ≤ m ≤ n and (m − 1) (n − 1) + 1 ≤ p ≤ (m − 1) m. We showed in previous papers that if p ≥ (m − 1) (n − 1) + 2 , then typical ranks of p × n × m -tensors over the real number field are p and p+1 if and only if there exists a non-singular bilinear map R m × R n → R m n − p . We also showed that the 'if' part is also valid in the case where p = (m − 1) (n − 1) + 1. In this paper, we consider the case where p = (m − 1) (n − 1) + 1 and show that the typical ranks of p × n × m -tensors over the real number field are p and p+1 in several cases including the case where there is no non-singular bilinear map R m × R n → R m n − p . In particular, we show that the 'only if' part of the above mentioned fact is not valid for the case p = (m − 1) (n − 1) + 1. [ABSTRACT FROM AUTHOR]

The adjacency matrix of a k-partite tournament for k ≥ 2 is represented as a (0 , 1) Boolean block matrix A with blocks A i j for 1 ≤ i , j ≤ k such that A i i is a zero matrix; A i j + A j i T is a matrix with all elements equal to 1 for i ≠ j where A j i T means the transpose of A j i . There is the smallest positive integer q such that A q + i (A T) q + i = A q + r + i (A T) q + r + i for some positive integer r and every nonnegative integer i. Then there is also the smallest positive integer p such that A q (A T) q = A q + p (A T) q + p . In this paper, we show that p ≤ 3 , and, further, if k = 2, then p ≤ 2. [ABSTRACT FROM AUTHOR]

This paper contributes to define one-sided versions of 'w-core inverse' introduced by the writer. Given any ∗ -ring R and a , w ∈ R , a is called right w-core invertible if there exists some x ∈ R satisfying awxa = a, a w x 2 = x and a w x = (a w x) ∗ . Several characterizations for this type of generalized inverses are given, and it is shown that a is right w-core invertible if and only if a is right w (a w) n − 1 -core invertible if and only if there exists a Hermitian element p such that pa = 0 and p + (a w) n is right invertible for any integer n ≥ 1 , in which case, the expression of right w-core inverses is given. Finally, it is proved that right w-core inverses are instances of right inverses along an element, right (b , c) -inverses and right annihilator (b , c) -inverses. As an application, the characterization for the Moore–Penrose inverse is given. [ABSTRACT FROM AUTHOR]

In this paper we completely solve the family of parametrised Thue equations where Fn is the n-th Fibonacci number. In particular, for any integer n ≥ 3 the Thue equation has only the trivial solutions (±1; 0); (0;∓1);∓(Fn; 1);∓(2n; 1). [ABSTRACT FROM AUTHOR]

Let R be a ring and n be a non-negative integer. In this paper, we introduce and study the notions of Gorenstein n-weak injective and Gorenstein n-weak flat modules by using the notion of special super finitely presented modules. On an arbitrary ring, we investigate the relationships between Gorenstein n-weak injective and Gorenstein n-weak flat modules. Among other results, we prove that any R-module admits a Gorenstein n-weak injective (resp. Gorenstein n-weak flat) cover and pre-envelope. Then, we deduce that the class of Gorenstein n-weak injective (resp. Gorenstein n-weak flat) R-modules coincides with that of two-degree Gorenstein n-weak injective (resp. two-degree Gorenstein n-weak flat) R-modules. [ABSTRACT FROM AUTHOR]

For integers and , denote by and the sums given by and respectively. In this paper, we deduce certain supercongruence relations for and. As particular cases, we give proofs of some conjectural supercongruences of Guo. [ABSTRACT FROM AUTHOR]