Combined bound-grid-factor constraints for enhancing RLT relaxations for polynomial programs

This paper studies the global optimization of polynomial programming problems using Reformulation-Linearization Technique (RLT)-based linear programming (LP) relaxations. We introduce a new class of bound-grid-factor constraints that can be judiciously used to augment the basic RLT relaxations in order to improve the quality of lower bounds and enhance the performance of global branch-and-bound algorithms. Certain theoretical properties are established that shed light on the effect of these valid inequalities in driving the discrepancies between RLT variables and their associated nonlinear products to zero. To preserve computational expediency while promoting efficiency, we propose certain concurrent and sequential cut generation routines and various grid-factor selection rules. The results indicate a significant tightening of lower bounds, which yields an overall reduction in computational effort for solving a test-bed of polynomial programming problems to global optimality in comparison with the basic RLT procedure as well as the commercial software BARON.     

A scalable optimization approach for fitting canonical tensor decompositions

Tensor decompositions are higher‐order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as CANDECOMP/PARAFAC (CP), which expresses a tensor as the sum of component rank‐one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience and web analysis. The task of computing CP, however, can be difficult. The typical approach is based on alternating least‐squares (ALS) optimization, but it is not accurate in the case of overfactoring. High accuracy can be obtained by using nonlinear least‐squares (NLS) methods; the disadvantage is that NLS methods are much slower than ALS. In this paper, we propose the use of gradient‐based optimization methods. We discuss the mathematical calculation of the derivatives and show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient‐based optimization methods are more accurate than ALS and faster than NLS in terms of total computation time. Copyright © 2011 John Wiley & Sons, Ltd.     

Cobalt ion-doped polyaniline,poly(N-methylaniline), and poly(N-ethylaniline): electrosynthesis and characterisation using electrochemical methods in acidic solutions

Cobalt ion (Co²⁺)-doped polyaniline (PANI-Co), poly(N-methylaniline) (PNMA-Co), and poly(N-ethylaniline) (PNEA-Co) films were synthesised electrochemically on a pencil graphite electrode (PGE) and their electrochemical properties were investigated for supercapacitor applications. The polymer film-coated electrodes (PGE/PANI-Co, PGE/PNMA-Co, and PGE/PNEA-Co) thus obtained were characterised by scanning electron microscopy (SEM) and different electrochemical methods. Cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) measurements were employed in 0.1 M H₂SO₄ solution to calculate the specific capacitance (C _S) values of the electrodes. The maximum C _S of 192.94 F g^?1, 139.83 F g^?1, and 47.12 F g^?1 were achieved for PGE/PANI-Co, PGE/PNMA-Co, and PGE/PNEA-Co at 1 mV s^?1, respectively. On the other hand, the charge/discharge stability of the electrodes was analysed using the repeating chronopotentiometry (RCP) method. The RCP measurements indicate that the electrodes could be used as an electrode active material for low voltage supercapacitor applications.     

On Rings Whose Reflexive Ideals are Principal

We call a prime Noetherian maximal order R a pseudo-principal ring if every reflexive ideal of R is principal. This class of rings is a broad class properly containing both prime Noetherian pri-(pli) rings and Noetherian unique factorization rings (UFRs). We show that the class of pseudo-principal rings is closed under formation of n × n full matrix rings. Moreover, we prove that if R is a pseudo-principal ring, then the polynomial ring R[x] is also a pseudo-principal ring. We provide examples to illustrate our results.     

Corrigendum to: Goldie Extending Modules

This corrigendum is written to correct an error in Corollary 2.5(ii) and an error in the proof of the converse of Theorem 2.7 of Akalan, Birkenmeier, and Tercan [1 Akalan , E. , Birkenmeier , G. F. , Tercan , A. ( 2009 ). Goldie extending modules . Comm. Algebra 37 : 663 – 683 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]].     

Classes of Almost Clean Rings

A ring is clean (almost clean) if each of its elements is the sum of a unit (regular element) and an idempotent. A module is clean (almost clean) if its endomorphism ring is clean (almost clean). We show that every quasi-continuous and nonsingular module is almost clean and that every right CS (i.e. right extending) and right nonsingular ring is almost clean. As a corollary, all right strongly semihereditary rings, including finite AW ^*-algebras and noetherian Leavitt path algebras in particular, are almost clean. We say that a ring R is special clean (special almost clean) if each element a can be decomposed as the sum of a unit (regular element) u and an idempotent e with aR?∩?eR?=?0. The Camillo-Khurana Theorem characterizes unit-regular rings as special clean rings. We prove an analogous theorem for abelian Rickart rings: an abelian ring is Rickart if and only if it is special almost clean. As a corollary, we show that a right quasi-continuous and right nonsingular ring is left and right Rickart. If a special (almost) clean decomposition is unique, we say that the ring is uniquely special (almost) clean. We show that (1) an abelian ring is unit-regular (equiv. special clean) if and only if it is uniquely special clean, and that (2) an abelian and right quasi-continuous ring is Rickart (equiv. special almost clean) if and only if it is uniquely special almost clean. Finally, we adapt some of our results to rings with involution: a *-ring is *-clean (almost *-clean) if each of its elements is the sum of a unit (regular element) and a projection (self-adjoint idempotent). A special (almost) *-clean ring is similarly defined by replacing “idempotent” with “projection” in the appropriate definition. We show that an abelian *-ring is a Rickart *-ring if and only if it is special almost *-clean, and that an abelian *-ring is *-regular if and only if it is special *-clean.     

Synthesis,characterization, spectroscopic,and thermal studies of imidazole complexes of metal benzenesulfonates. Crystal structure of [M(imH)<Subscript>3</Subscript>(H<Subscript>2</Subscript>O)<Subscript>3</Subscript>]·(BS)<Subscript>2</Subscript> [M=Ni(II) and Co(II)]

Four novel transition metal benzenesulfonate (BS) complexes of imidazole (im) with a general formula [M(imH)₃(H₂O)₃]·(BS)₂ [M=Mn(II) (1), Ni(II) (2), Co(II) (3)] and [Cu(BS)(imH)₃]·(BS) (4) have been synthesized and characterized by physicochemical and spectroscopic methods. The complexes 2 and 3 have also been characterized by single X-ray diffraction technique. The BS anion in complexes 1–3 acts as a counter anion, while in complex 4, it acts as both ligand and counter anion. The Ni and Co complexes are isomorphous, crystallizing in the monoclinic crystal system with C2/c space group. Each metal(II) atom in 2 and 3 is octahedrally coordinated by three imidazole and three aqua ligands, adopting a mer-coordination mode with Ni(II) or Co(II) centers. In both 2 and 3, the H2C atom has bifurcated donor (O3 and O5) atoms, forming a bifurcated hydrogen bond. This hydrogen bond links the complex cation and BS anion, forming one-dimensional hydrogen-bonded supramolecular chains. The complexes exhibit different decomposition characteristics. Magnetic susceptibility measurement shows that complex 3 has orbital interactions.     

Synthesis and Antinociceptive Effect of Some Thiazole-Piperazine Derivatives: Involvement of Opioidergic System in the Activity

In this study, we aimed to design and synthesize novel molecules carrying both the thiazole and piperazine rings in their structures and to investigate their antinociceptive activity. Targeted compounds were obtained by reacting thiosemicarbazide derivative and appropriate 2-bromoacetophenone in ethanol. The structures of the obtained compounds were determined using data from various spectroscopic methods (IR, ¹H-NMR, ¹³C-NMR, and LCMSMS). Experimental data from in vivo tests showed that test compounds 3a–3c, 3f, and 3g (50 mg/kg) significantly prolonged reaction times of animals in tail-clip and hot-plate tests compared to the controls, indicating that these compounds possess centrally mediated antinociceptive activities. Furthermore, these compounds reduced the number of writhing behaviors in the acetic acid-induced writhing tests, showing that the compounds also possess peripheral antinociceptive activity. In the mechanistic studies, naloxone pre-treatments abolished the antinociceptive activities of compounds 3a–3c, 3f, and 3g, indicating that opioidergic mechanisms were involved in their antinociceptive effects. Molecular docking studies demonstrating significant interactions between the active compounds and µ- and δ-opioid receptor proteins supported the pharmacological findings. This study is the first showing that molecules designed to bear thiazole and piperazine moieties together on their structure exert centrally and peripherally mediated antinociceptive effects by activating the opioid system.     

Weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) for decomposition of multiway arrays: applications on certain chemical system data sets

This work focuses on the utilization of a very recently developed decomposition method, weighted tridiagonal matrix enhanced multivariance products representation (WTMEMPR) which can be equivalently used on continuous functions, and, multiway arrays after appropriate unfoldings. This recursive method has been constructed on the Bivariate EMPR and the remainder term of each step therein has been expanded into EMPR from step to step until no remainder term appears in one of the consecutive steps. The resulting expansion can also be expressed in a three factor product representation whose core factor is a tridiagonal matrix. The basic difference and novelty here is the non-constant weight utilization and the applications on certain chemical system data sets to show the efficiency of the WTMEMPR truncation approximants.     

Group rings which are G-Dedekind prime rings

Let R be a commutative Noetherian domain and A be a polycyclic-by-finite group. In this paper, it is determined, in terms of properties of R and A when the group ring R[A] is a G-Dedekind prime ring.