In this paper, we characterize the classes (L,Lk) , (Lk,L) and (L∞,Lk) 1 ≤ k < ∞, of all four dimensional infinite matrices, where Lk L∞ are spaces absolutely k-summable bounded double sequences, respectively. Using them, establish some relations between N, pn, qn p′ n, q′n summability methods which extend results Bosanquet (1950), Sarıg¨ol (1993), Bor (1995), Sunouchi (1949) to methods, giv...

Abstract: The Lin and Kernighan’s algorithm (LK) for the single objective Traveling Salesman Problem (TSP) is one of the most efficient heuristics for the symmetric case. Although many algorithms for the TSP were extended to the multi-objective version of the problem (MTSP), the LK was still not fully explored. Works that applied the LK for the MTSP were driven to weighted sum versions of the p...

Proteomics was employed to investigate the molecular mechanisms of apoplastic response to potassium(K)-deficiency in cotton. Low K (LK) treatment significantly decreased the K and protein contents of xylem sap. Totally, 258 peptides were qualitatively identified in the xylem sap of cotton seedlings, of which, 90.31% were secreted proteins. Compared to the normal K (NK), LK significantly decreas...

In this section we will talk about some simple algorithms for looking up items in a sorted list. Broadly speaking, an algorithm is a group of instructions that completely characterize the process of converting a set of inputs into desired outputs. To illustrate this concept, we shall solve a basic search problem. Let L = {l1, l2, . . . , lK} denote a set of ordered objects, where lk precedes lk...

Dear Sir: In this letter we attempt to resolve a discrepancy on the effect of trypsin on the sensitivity of low potassium (LK) sheep red blood cells to the anti-L antibody. We had reported the failure of trypsinization to abolish completely sensitivity to the antibody (I). More recently Lauf et al. published in this journal the observation that trypsin could indeed eliminate all sensitivity (10...

We show that if E is an arbitrary acyclic graph then the Leavitt path algebra LK(E) is locally K-matricial; that is, LK(E) is the direct union of subalgebras, each isomorphic to a finite direct sum of finite matrix rings over the fieldK. As a consequence we get our main result, in which we show that the following conditions are equivalent for an arbitrary graph E: (1) LK (E) is von Neumann regu...

Abstract In this paper, we consider the k -Fibonacci and k -Lucas sequences {Fk,n}n∈N and {Lk,n}n∈N . Let A = Cr(Fk,0, Fk,1, · · · , Fk,n−1) and B = Cr(Lk,0, Lk,1, · · · , Lk,n−1) be r -circulant matrices. Afterwards, we give upper and lower bounds for the spectral norms of matrices A and B. In addition, we obtain some bounds for the spectral norms of Hadamard and Kronecker products of these ma...

We characterise directed graphs consisting of disjoint cycles via their talented monoids. show that a graph E consists precisely when its monoid TE has certain Jordan-Hölder composition series. These are whose associated Leavitt path algebras Lk(E) have finite Gelfand-Kirillov dimension (GKdim). this can be determined as the length ideal series monoid. Since is positive cone graded Grothendieck...

The vasoactive compound bradykinin (BK) is liberated by proteolytic cleavage from high molecular weight kininogen (HK) and low molecular weight kininogen (LK). Expression of kininogens on cell surface receptors may affect the delivery of BK at sites of inflammation. Therefore, we investigated whether BK itself alters the expression of binding sites for its parent molecules, HK and LK, on the su...

This paper investigates a non-commutative first-order sequent calculus NCLK. For that, this paper extends a non-commutative positive fragment to a full first-order sequent calculus LK− having antecedent-grouping and no right exchange rule. This paper shows (1) NCLK is equivalent to LJ, (2) NCLK with the exchange rule is equivalent to LK, (3) LK− is equivalent to LJ, and (4) translations between...