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Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as the WTW and ZTZ factorizations of a symmetric positives definite matrix. We also describe the QZ and the QW factorizations, withQ orthogonal, and show how to appropriate the parameters of the ABS algorithms to compute these factorizations  

Let G be a graph. A well-known theorem due to Tutte states that G contains {1, 2}-factor if and only if for every subset S⊆. V(G), i(G. S). ≤. |. S|, where i(G. S) denotes the number of isolated vertices of G. S. In this note we give a new proof for this result using permanents  

In 1984, Abaffy, Broyden, and Spediacto (ABS) introduced a class of the so-called ABS algorithms to solve systems of real linear equations. Later, the scaled ABS algorithm, the extended ABS algorithm, the block ABS algorithm, and the integer ABS algorithm were introduced leading to various well-known matrix factorizations. Here, we present a generalization of ABS algorithms containing all matrix factorizations such as triangular, WZ, and ZW. We present the octant interlocking factorization and show that the generalized ABS algorithm is more general to produce the octant interlocking factorization. Copyright © 2022 Via Medica  

Calendula alata, Amaranthus chlorostachys and Chenopodium album plants were tested for their potential to uptake and accumulate stable cesium and lead from solutions in a period of 15 days. The plants were grown hydroponically and placed in solutions containing CsCl and Pb(C2H3O2)2 at three different concentrations (0.6, 2 and 5 mg L-1). Cs transfer factors in different solutions were more than 1 with the highest level of 2.45 for 2 mg L-1 of CsCl and Pb(C2H3O2)2 in mixed solution. According to its uptake from the environment, cesium effect on anatomical and ontogenical structure of plant was studied. Aerial organs of Chenopodium album were investigated for modifications studies. Observation... 

Motorcycles are the third most common means of transportation in the megacity of Tehran. Hence, measurements of emission factors are essential for Tehran motorcycle fleets. In this study, 60 carburetor motorcycles of various mileages and engine displacement volumes were tested in a chassis dynamometer laboratory according to cold start Euro-3 emissions certification test procedures. For almost all of the tested samples, the average carbon monoxide (CO) emission factors were about seven times higher than the limits for Euro-3 certification. No motorcycle fell within the Euro-3 certification limit on CO emissions. 125 cc engine displacement volume motorcycles, which are dominant in Tehran,... 

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm. © 2018 Elsevier B.V  

For a set S of positive integers, a spanning subgraph F of a graph G is called an S-factor of G if degF(x) ∈ S for all vertices x of G, where degF(x) denotes the degree of x in F. We prove the following theorem on {a, b}-factors of regular graphs. Let r ≥ 5 be an odd integer and k be either an even integer such that 2 ≤ k < r/2 or an odd integer such that r/3 ≤ k < r/2. Then every r-regular graph G has a {k, r-k}-factor. Moreover, for every edge e of G, G has a {k, r-k}-factor containing e and another {k, r-k}-factor avoiding e  

Let G be a graph and S be a set of non-negative integers. By an S-degree free spanning forest of G we mean a spanning forest of G with no vertex degree in S. In this paper we study the existence of {0,2}-degree free spanning forests in graphs. We show that if G is a graph with minimum degree at least 4, then there exists a {0,2}-degree free spanning forest. Moreover, we show that every 2-connected graph with maximum degree at least 5 admits a {0,2}-degree free spanning forest, and every 3-connected graph admits a {0,2}-degree free spanning forest  

Let A be an n-square non-negative matrix. If A contains no s × t zero submatrix, where s + t = n, then it is called fully indecomposable. Moreover, a graph G is said to be fully indecomposable if its adjacency matrix is fully indecomposable. In this paper we provide some necessary and sufficient conditions for a graph to be fully indecomposable. Among other results we prove that a regular connected graph is fully indecomposable if and only if it is not bipartite. © 2017 University of Calgary  

Let G be a 2k-edge-connected graph with 𝑘 ≥ 0 and let 𝐿(𝑣) ⊆ {𝑘,…, 𝑑𝐺(𝑣)} for every 𝑣 ∈ 𝑉 (𝐺). A spanning subgraph F of G is called an L-factor, if 𝑑𝐹 (𝑣) ∈ 𝐿(𝑣) for every 𝑣 ∈ 𝑉 (𝐺). In this article, we show that if (Formula presented.) for every 𝑣 ∈ 𝑉 (𝐺), then G has a k-edge-connected L-factor. We also show that if 𝑘 ≥ 1 and (Formula presented.) for every 𝑣 ∈ 𝑉 (𝐺), then G has a k-edge-connected L-factor. © 2018 Wiley Periodicals, Inc  

The response surface methodology (RSM) is firstly employed to investigate the geometric and flow parameters on heat transfer, pressure drop and thermal performance of sinusoidal wavy channels with different phase shifts. The investigated flow and geometric parameters are axial Reynolds number 1106