Constrained variational refinement

A non-uniform, variational refinement scheme is presented for computing piecewise linear curves that minimize a certain discrete energy functional subject to convex constraints on the error from interpolation. Optimality conditions are derived for both the fixed and free-knot problems. These conditions are expressed in terms of jumps in certain (discrete) derivatives. A computational algorithm is given that applies to constraints whose boundaries are either piecewise linear or spherical. The results are applied to closed periodic curves, open curves with various boundary conditions, and (approximate) Hermite interpolation.     

On some questions related to the Gauss conjecture for function fields

We show that, for any finite field Fq, there exist infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is a separable polynomial. As pointed out by Anglès, this is a necessary condition for the existence, for any finite field Fq, of infinitely many real function fields over Fq with ideal class number one (the so-called Gauss conjecture for function fields). We also show conditionally the existence of infinitely many real quadratic function fields over Fq such that the numerator of their zeta function is an irreducible polynomial.     

Some explicit upper bounds for residues of zeta functions of number fields taking into account the behavior of the prime 2

We recall the known explicit upper bounds for the residue at s = 1 of the Dedekind zeta function of a number field K. Then, we improve upon these previously known upper bounds by taking into account the behavior of the prime 2 in K. We finally give several examples showing how such improvements yield better bounds on the absolute values of the discriminants of CM-fields of a given relative class number. In particular, we will obtain a 4,000-fold improvement on our previous bound for the absolute values of the discriminants of the non-normal sextic CM-fields with relative class number one.     

Optimal multiple-objective resource allocation using hybrid particle swarm optimization and adaptive resource bounds technique

The multiple-objective resource allocation problem (MORAP) seeks for an allocation of resource to a number of activities such that a set of objectives are optimized simultaneously and the resource constraints are satisfied. MORAP has many applications, such as resource distribution, project budgeting, software testing, health care resource allocation, etc. This paper addresses the nonlinear MORAP with integer decision variable constraint. To guarantee that all the resource constraints are satisfied, we devise an adaptive-resource-bound technique to construct feasible solutions. The proposed method employs the particle swarm optimization (PSO) paradigm and presents a hybrid execution plan which embeds a hill-climbing heuristic into the PSO for expediting the convergence. To cope with the optimization problem with multiple objectives, we evaluate the candidate solutions based on dominance relationship and a score function. Experimental results manifest that the hybrid PSO derives solution sets which are very close to the exact Pareto sets. The proposed method also outperforms several representatives of the state-of-the-art algorithms on a simulation data set of the MORAP.     

Theoretical Study of Substituent Effects on Geometric and Spectroscopic Parameters (IR, 13C, 29Si NMR) and Energy Decomposition Analysis of the Bonding in Molybdenum Silylidyne Complexes CpMo(CO)2(≡Si‐para‐C6H4X)

In this study, we report the substituent effect on the structures, frontier orbital analysis, and spectroscopic properties (IR , ¹³C , ²⁹Si NMR ) in the molybdenum silylidyne complexes CpMo (CO )₂(≡Si‐para ‐C₆H₄X ) (X = H, F, Cl, CN , NO₂ , Me, OMe , NH₂ , NHMe ) using MPW1PW91 quantum chemical calculations. The calculated structural parameters and spectral parameters are compatible with the experimental values in similar complexes. The nature of the chemical bond between the [Cp(OC ) ₂Mo ]⁻ and [Si‐para ‐C₆H₄X ]⁺ fragments was explored with energy decomposition analysis (EDA ). The percentage composition in terms of the defined groups of frontier orbitals for CpMo (CO )₂(≡Si‐para ‐C₆H₄X ) complexes was investigated to explore the character of the metal–ligand bonds. The linear correlations between the properties and Hammett constants (σ _p) were illustrated. Natural bond orbital analysis (NBO ) was used to illustrate the electronic structure of the complexes.     

NMR spectral assignment of 2α- and 3β-methylhopanes and evidence for boat conformation in D ring of 17α(H),21α(H)-hopanes

The full (1)H and (13)C NMR chemical shift assignment of 2α-methyl-17α(H),21β(H)-hopane is presented. This compound is formed in mature sediments from biogenic sources of 2β-methyl-17β(H),21β(H)-hopanoids, which include several cyanobacteria. In addition, full (1)H and (13)C NMR chemical shift data of all four 17,21 isomers of 3β-methylhopane have been assigned. The thermodynamically most stable 3β-configuration corresponds to that found in bacterial sources. The data presented here suggest minor corrections to the (13)C chemical assignments reported earlier for 17α(H)-hopanes. Moreover, spectral evidence indicates an unexpected ring-D boat conformation of 17α(H),21α(H)-hopanes, which may serve to explain the steric strain reported for this isomer.     

TRPC3 cation channel plays an important role in proliferation and differentiation of skeletal muscle myoblasts

During membrane depolarization associated with skeletal excitation-contraction (EC) coupling, dihydropyridine receptor [DHPR, a L-type Ca²⁺ channel in the transverse (t)-tubule membrane] undergoes conformational changes that are transmitted to ryanodine receptor 1 [RyR1, an internal Ca²⁺-release channel in the sarcoplasmic reticulum (SR) membrane] causing Ca²⁺ release from the SR. Canonical-type transient receptor potential cation channel 3 (TRPC3), an extracellular Ca²⁺-entry channel in the t-tubule and plasma membrane, is required for full-gain of skeletal EC coupling. To examine additional role(s) for TRPC3 in skeletal muscle other than mediation of EC coupling, in the present study, we created a stable myoblast line with reduced TRPC3 expression and without α1_SDHPR (MDG/TRPC3 KD myoblast) by knock-down of TRPC3 in α1_SDHPR-null muscular dysgenic (MDG) myoblasts using retrovirus-delivered small interference RNAs in order to eliminate any DHPR-associated EC coupling-related events. Unlike wild-type or α1_SDHPR-null MDG myoblasts, MDG/TRPC3 KD myoblasts exhibited dramatic changes in cellular morphology (e.g., unusual expansion of both cell volume and the plasma membrane, and multi-nuclei) and failed to differentiate into myotubes possibly due to increased Ca²⁺ content in the SR. These results suggest that TRPC3 plays an important role in the maintenance of skeletal muscle myoblasts and myotubes.     

Investigation of the optical limiting properties of acid blue29 in various solvents

The optical limiting properties of acid blue29 solutions in different solvents are investigated. Experiments are performed using a CW He-Ne Laser beam at 632.8 nm wavelength and 35 mW power. The strength of the optical limiting action is dramatically influenced by the solvent. Multiple diffraction rings were observed when the samples were exposed to laser radiation. The effect of concentration, solvent and laser intensity on the diffraction rings are studied experimentally. Our results show that the nonlinear refraction is the dominant mechanism to explain the optical limiting behavior in acid blue29.     

Anisotropy and FOMP in Tb3 (Fe28−xCox) V1.0 (x=0, 3 and 6) compounds

In this work, the structural and magnetic properties of Tb₃ (Fe_28−xCo_x) V_1.0 (x=0, 3, 6) compounds have been investigated. The structural characterization of compounds by X-ray powder diffraction is an evidence for a monoclinic Nd₃(Fe, Ti)₂₉-type structure (A2/m space group). The refined lattice parameters a and b (but not c) and the unit cell volume V, obtained from the XRD data by the Rietveld method, are found to decrease with increasing Co concentration. The unit cell parameters behavior has been attributed to the smaller Co atoms and a preferential substitution of Fe by Co. The anisotropy field (H_a) as well as critical field (H_cr) was measured using the singular point detection (SPD) technique from 5 to 300 K in a pulsed magnetic field of up to 30 T. At T=5 K, a FOMP of type 2 was observed for all samples and persists at all temperatures up to 300 K. For sample x=0, H_cr=10.6 and 2.0 T at 5 and 300 K, respectively, is equal to that reported earlier. The occurrence of canting angles between the magnetic sublattices during the magnetization process instead of high-order anisotropy contributions (at room temperature are usually negligible) has been considered to explain the survival of the FOMP at room temperature. The anisotropy and critical fields behave differently for samples with x=0, 3 compared with x=6. The observed behavior has been related to the fact that the Co substitution for Fe takes place with a preferential entrance in the inequivalent crystallographic sites of the 3:29 structure. The contribution of the Tb-sublattice in the Tb₃(Fe, V)₂₉ compound with uniaxial anisotropy has been scaled from the anisotropy field measured on a Y₃(Fe, V)₂₉ single crystal with easy plane anisotropy.     

The constrained inverse eigenvalue problem and its approximation for normal matrices

In this paper, the constrained inverse eigenvalue problem and associated approximation problem for normal matrices are considered. The solvability conditions and general solutions of the constrained inverse eigenvalue problem are presented, and the expression of the solution for the optimal approximation problem is obtained.