On Balazard,Saias, and Yor’s equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)$S\left(t\right)$ in the theory of the Riemann zeta-function.     

On optimality conditions for vector variational inequalities

Optimality conditions for weak efficient, global efficient and efficient solutions of vector variational inequalities with constraints defined by equality, cone and set constraints are derived. Under various constraint qualifications, necessary optimality conditions for weak efficient, global efficient and efficient solutions in terms of the Clarke and Michel–Penot subdifferentials are established. With assumptions on quasiconvexity of constraint functions sufficient optimality conditions are also given.     

Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints

In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.

     

Plasma brominated polymer particles as grafting substrate for thiol‐terminated telomers

A combined surface activation and “grafting to” strategy was developed to convert divinylbenzene particles into weak cation exchangers suitable for protein separation. The initial activation step was based on plasma modification with bromoform, which rendered the particles amenable to further reaction with nucleophiles by introducing Br to a surface content of 11.2 atom‐%, as determined by X‐ray photoelectron spectroscopy. Grafting of thiol‐terminated glydicyl methacrylate telomers to freshly plasma activated surfaces was accomplished without the use of added initiator, and the grafting was verified both by reduction in bromine content and the appearance of sulfur‐carbon linkages, showing that the surface grafts were covalently bonded. Following grafting the attached glydicyl methacrylate telomer tentacles were further modified by a two‐step procedure involving hydrolysis to 2,3‐hydroxypropyl groups and conversion of hydroxyl groups to carboxylate functionality by succinic anhydride. The final material was capable of baseline separating four model proteins in 3 min by gradient cation exchange chromatography in a fully aqueous eluent.     

New statistical method for detection and quantification ofrespiratory sinus arrhythmia

A statistical method with the advantages of 1) enabling graphical representation of within-respiratory cycle heart rate variations, 2) detecting the presence of respiratory sinus arrhythmia (RSA) in a moving window, and 3) providing breath-by-breath RSA amplitude and phase obtained from the fitting of a sinusoid to the instantaneous relative heart rate is presented.     

A systematic approach to the construction of bandwidth-efficient multidimensional trellis codes

We present a unified approach to the construction of multidimensional trellis codes that have small constellation expansion ratio (CER) and small peak-to-average power ratio (PAR) and hence are of high bandwidth efficiency. In the approach, we extend Wei's (1987) construction to dimensionalities other than a power of two and propose a low-complexity encoder. We also present a general partition technique that gives geometrically uniform partitions with a good distance profile. The proposed method can generate many good codes including previously reported Ungerboeck codes, Gallager-Calderbank-Sloane codes, and Wei codes with quadrature amplitude modulation signals. Some newly discovered six-dimensional trellis codes are compared with these known codes on their CER, PAR, effective coding gain, and encoder/decoder complexities.     

Spectrally Adjustable Picosecond Dye Laser Pulses Generated with Nanosecond Nitrogen Lasers

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