Jacobi forms and differential operators

We affirmatively answer a question due to S. Bocherer concerning the feasibility of removing one differential operator from the standard collection of m + 1 of them used to embed the space of Jacobi forms of weight 2 and index m into several pieces of elliptic modular forms. (C) 2014 Elsevier Inc. All rights reserved.

L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains

It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite-dimensional inner product spaces. The representations, and the induced bundles, have composition series with irreducible factors. We write down an equivariant constant coefficient differential operator that intertwines the bundle with the direct sum of its irreducible factors. As an application, we show that in the case of the closed unit ball in C-n all homogeneous n-tuples of Cowen-Douglas operators are similar to direct sums of certain basic n-tuples. (c) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Mycobacterium tuberculosis groE promoter controls the expression of the bicistronic groESL1 operon and shows differential regulation under stress conditions

Heat shock promoters of mycobacteria are strong promoters that become rapidly upregulated during macrophage infection and thus serve as valuable candidates for expressing foreign antigens in recombinant BCG vaccine. In the present study, a new heat shock promoter controlling the expression of the groESL1 operon was identified and characterized. Mycobacterium tuberculosis groESL1 operon codes for the immunodominant 10 kDa (Rv3418c, GroES/Cpn10/Hsp10) and 60 kDa (Rv3417c, GroEL1/Cpn60.1/Hsp60) heat shock proteins. The basal promoter region was 115 bp, while enhanced activity was seen only with a 277-bp fragment. No promoter element was seen in the groES-groEL1 intergenic region. This operon codes for a bicistronic mRNA transcript as determined by reverse transcriptase-PCR and Northern blot analysis. Primer extension analysis identified two transcriptional start sites (TSSs) TSS1 (-236) and TSS2 (-171), out of which one (TSS2) was heat inducible. The groE promoter was more active than the groEL2 promoter in Mycobacterium smegmatis. Further, it was found to be differentially regulated under stress conditions, while the groEL2 promoter was constitutive.

Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

The complementation of yeast with human or Plasmodium falciparum Hsp90 confers differential inhibitor sensitivities

Developing novel drugs against the unicellular parasite Plasmodium is complicated by the paucity of simple screening systems. Heat-shock proteins are an essential class of proteins for the parasite's cyclical life style between different cellular milieus and temperatures. The molecular chaperone Hsp90 assists a large variety of proteins, but its supporting functions for many proteins that are important for cancer have made it into a well-studied drug target. With a better understanding of the differences between Hsp90 of the malarial parasite and Hsp90 of its human host, new therapeutic options might become available. We have generated a set of isogenic strains of the budding yeast Saccharomyces cerevisiae where the essential yeast Hsp90 proteins have been replaced with either of the two human cytosolic isoforms Hsp90 alpha or Hsp90 beta, or with Hsp90 from Plasmodium falciparum (Pf). All strains express large amounts of the Flag-tagged Hsp90 proteins and are viable. Even though the strain with Pf Hsp90 grows more poorly, it provides a tool to reconstitute additional aspects of the parasite Hsp90 complex and its interactions with substrates in yeast as a living test tube. Upon exposure of the set of Hsp90 test strains to the two Hsp90 inhibitors radicicol (Rd) and geldanamycin (GA), we found that the strain with Pf Hsp90 is relatively more sensitive to GA than to Rd compared to the strains with human Hsp90's. This indicates that this set of yeast strains could be used to screen for new Pf Hsp90 inhibitors with a wider therapeutic window.

Oestrogenic regulation and differential expression of WNT4 in the bonnet monkey and rodent epididymis

A role for oestrogen in regulating fluid reabsorption in the monkey epididymis was recently demonstrated. Here, these Studies are extended to identify potential oestrogen-regulated proteins in the cauda region of monkey epididymis treated with vehicle and oestrogen receptor antagonist (ICI 182780). Two-dimensional electrophoretic analysis was used to identify the proteins. The results indicated down-regulation of WNT4 in the ICI-182780-treated monkey cauda. In addition. the Wnt4f mRNA concentration was also reduced in the caput regions of ICI-182780-treated rats and oestrogen receptor knockout mice. WNT4 is a key regulator of gonadal differentiation in humans and mice and plays a pivotal role in early mouse embryogenesis. The results of the present Study establish the presence of WNT4 in the monkey epididymis and its regulation by oestrogen, and Suggest a role for WNT4 in maintaining epididymal homeostasis.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

Low-intensity differential photocapacitance of MOS structures

Some new observations on the phenomenon of photocapacitane on n-type silicon MOS structures under low intensities of illumination are reported. The difference between the illuminated and dark C---characteristics is automatically followed as a function of the applied bias thereby obtaining the differential photocapacitance and the resulting characteristics has been termed as the Low Intensity Differential Photocapacitance (LIDP). For an MOS capacitor, the LIDP characteristics is seen to go through a well defined maximum. The phenomenon has been investigated under different ambient conditions like light intensity, temperature, dependance of the frequency of the light etc. and it has been found that the phenomenon is due to a band excband excitation. In this connection, a novel sensitive technique for the measurement of the capacitance based upon following the frequency changes of a tank circuit is also described in some detail. It is also shown that the phenomenon can be understood by a simple theoretical model.

A Novel Operator-Splitting Technique for One-Dimensional Laminar Premixed Flames

This paper is concerned the calculation of flame structure of one-dimensional laminar premixed flames using the technique of operator-splitting. The technique utilizes an explicit method of solution with one step Euler for chemistry and a novel probabilistic scheme for diffusion. The relationship between diffusion phenomenon and Gauss-Markoff process is exploited to obtain an unconditionally stable explicit difference scheme for diffusion. The method has been applied to (a) a model problem, (b) hydrazine decomposition, (c) a hydrogen-oxygen system with 28 reactions with constant Dρ 2 approximation, and (d) a hydrogen-oxygen system (28 reactions) with trace diffusion approximation. Certain interesting aspects of behaviour of the solution with non-unity Lewis number are brought out in the case of hydrazine flame. The results of computation in the most complex case are shown to compare very favourably with those of Warnatz, both in terms of accuracy of results as well as computational time, thus showing that explicit methods can be effective in flame computations. Also computations using the Gear-Hindmarsh for chemistry and the present approach for diffusion have been carried out and comparison of the two methods is presented.

Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

A multi-microprocessor architecture for solving partial differential equations

This paper presents the architecture of a fault-tolerant, special-purpose multi-microprocessor system for solving Partial Differential Equations (PDEs). The modular nature of the architecture allows the use of hundreds of Processing Elements (PEs) for high throughput. Its performance is evaluated by both analytical and simulation methods. The results indicate that the system can achieve high operation rates and is not sensitive to inter-processor communication delay.

Application of Haar functions for transmission line and transformer differential protection

The development of algorithms, based on Haar functions, for extracting the desired frequency components from transient power-system relaying signals is presented. The applications of these algorithms to impedance detection in transmission line protection and to harmonic restraint in transformer differential protection are discussed. For transmission line protection, three modes of application of the Haar algorithms are described: a full-cycle window algorithm, an approximate full-cycle window algorithm, and a half-cycle window algorithm. For power transformer differential protection, the combined second and fifth harmonic magnitude of the differential current is compared with that of fundamental to arrive at a trip decision. The proposed line protection algorithms are evaluated, under different fault conditions, using realistic relaying signals obtained from transient analysis conducted on a model 400 kV, 3-phase system. The transformer differential protection algorithms are also evaluated using a variety of simulated inrush and internal fault signals.

An Online Implementable Differential Evolution Tuned Optimal Guidance Law

This paper proposes a novel application of differential evolution to solve a difficult dynamic optimisation or optimal control problem. The miss distance in a missile-target engagement is minimised using differential evolution. The difficulty of solving it by existing conventional techniques in optimal control theory is caused by the nonlinearity of the dynamic constraint equation, inequality constraint on the control input and inequality constraint on another parameter that enters problem indirectly. The optimal control problem of finding the minimum miss distance has an analytical solution subject to several simplifying assumptions. In the approach proposed in this paper, the initial population is generated around the seed value given by this analytical solution. Thereafter, the algorithm progresses to an acceptable final solution within a few generations, satisfying the constraints at every iteration. Since this solution or the control input has to be obtained in real time to be of any use in practice, the feasibility of online implementation is also illustrated.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.