Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified "half-range" quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.

Discrete-Time Controlled Markov Processes with Average Cost Criterion: A Survey

This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T-2) where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF). (C) 2013 Published by Elsevier Ltd. on behalf of The Franklin Institute

Alternative Formulation of the Discrete Linear Quadratic Regulator (DLQR)

In this paper, an alternative apriori and aposteriori formulation has been derived for the discrete linear quadratic regulator (DLQR) in a manner analogous to that used in the discrete Kalman filter. It has been shown that the formulation seamlessly fits into the available formulation of the DLQR and the equivalent terms in the existing formulation and the proposed formulation have been identified. Thereafter, the significance of this alternative formulation has been interpreted in terms of the sensitivity of the controller performances to any changes in the states or to changes in the control inputs. The implications of this alternative formulation to adaptive controller tuning have also been discussed.

Identification of a discrete intermediate in the assembly disassembly of physalis mottle tymovirus through mutational analysis

Assembly intermediates of icosahedral viruses are usually transient and are difficult to identify. In the present investigation, site-specific and deletion mutants of the coat protein gene of physalis mottle tymovirus (PhMV) were used to delineate the role of specific amino acid residues in the assembly of the virus and to identify intermediates in this process. N-terminal 30, 34, 35 and 39 amino acid deletion and single C-terminal (N188) deletion mutant proteins of PhMV were expressed in Escherichia coli. Site-specific mutants H69A, C75A, W96A, D144N, D144N-T151A, K143E and N188A were also constructed and expressed. The mutant protein lacking 30 amino acid residues from the N terminus self-assembled to T = 3 particles in vivo while deletions of 34, 35 and 39 amino acid residues resulted in the mutant proteins that were insoluble. Interestingly, the coat protein (pR PhCP) expressed using pRSET B vector with an additional 41 amino acid residues at the N terminus also assembled into T = 3 particles that were more compact and had a smaller diameter. These results demonstrate that the amino-terminal segment is flexible and either the deletion or addition of amino acid residues at the N terminus does not affect T = 3 capsid assembly, in contrast, the deletion of even a single residue from the C terminus (PhN188 Delta 1) resulted in capsids that were unstable. These capsids disassembled to a discrete intermediate with a sedimentation coefficent of 19.4 S. However, the replacement of C-terminal asparagine 188 by alanine led to the formation of stable capsids. The C75A and D144N mutant proteins also assembled into capsids that were as stable as the pR PhCP, suggesting that C75A and D144 are not crucial for the T = 3 capsid assembly. pR PhW96A and pR PhD144N-T151A mutant proteins failed to form capsids and were present as heterogeneous aggregates. Interestingly, the pR PhK143E mutant protein behaved in a manner similar to the C-terminal deletion protein in forming unstable capsids. The intermediate with an s value of 19.4 S was the major assembly product of pR PhH69A mutant protein and could correspond to a 30mer. It is possible that the assembly or disassembly is arrested at a similar stage in pR PhN188 Delta 1, pR PhH69A and pR PhK143E mutant proteins.

A global convergence criterion for discrete-time multivariable adaptive systems

The paper deals with the basic problem of adjusting a matrix gain in a discrete-time linear multivariable system. The object is to obtain a global convergence criterion, i.e. conditions under which a specified error signal asymptotically approaches zero and other signals in the system remain bounded for arbitrary initial conditions and for any bounded input to the system. It is shown that for a class of up-dating algorithms for the adjustable gain matrix, global convergence is crucially dependent on a transfer matrix G(z) which has a simple block diagram interpretation. When w(z)G(z) is strictly discrete positive real for a scalar w(z) such that w-1(z) is strictly proper with poles and zeros within the unit circle, an augmented error scheme is suggested and is proved to result in global convergence. The solution avoids feeding back a quadratic term as recommended in other schemes for single-input single-output systems.

Applying pure mathematics: mathematics in the natural sciences

The book of nature is written in the language of mathematics. This quotation, attributed to Galileo, seemed to hold to an unreasonable1 extent in the era of quantum mechanics.

Optimal popular matchings

In this paper we consider the problem of computing an “optimal” popular matching. We assume that our input instance View the MathML source admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness in which case we are required to return a fair popular matching. We show an O(n2+m) algorithm for this problem, assuming that the preference lists are strict, where m is the number of edges in G and n is the number of applicants.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

A playful side to twelfth-century mathematics

As editors of the book Lilavati's Daughters: The Women Scientists of India, reviewed by Asha Gopinathan (Nature 460, 1082; 2009), we would like to elaborate on the background to its title. Lilavati was a mathematical treatise of the twelfth century, composed by the mathematician and astronomer Bhaskaracharya (1114–85) — also known as Bhaskara II — who was a teacher of repute and author of several other texts. The name Lilavati, which literally means 'playful', is a surprising title for an early scientific book. Some of the mathematical problems posed in the book are in verse form, and are addressed to a girl, the eponymous Lilavati. However, there is little real evidence concerning Lilavati's historicity. Tradition holds that she was Bhaskaracharya's daughter and that he wrote the treatise to console her after an accident that left her unable to marry. But this could be a later interpolation, as the idea was first mentioned in a Persian commentary. An alternative view has it that Lilavati was married at an inauspicious time and was widowed shortly afterwards. Other sources have implied that Lilavati was Bhaskaracharya's wife, or even one of his students — raising the possibility that women in parts of the Indian subcontinent could have participated in higher education as early as eight centuries ago. However, given that Bhaskara was a poet and pedagogue, it is also possible that he chose to address his mathematical problems to a doe-eyed girl simply as a whimsical and charming literary device.

Contribution from unresolved discrete sources to the extragalactic gamma-ray background (EGRB)

The origin of the extragalactic gamma-ray background (EGRB) is still an open question, even nearly forty years after its discovery. The emission could originate either from truly diffuse processes or from unresolved point sources. Although the majority of the 271 point sources detected by EGRET (Energetic Gamma Ray Experiment Telescope) are unidentified, of the identified sources, blazars are the dominant candidates. Therefore, unresolved blazars may be considered the main contributor to the EGRB, and many studies have been carried out to understand their distribution, evolution and contribution to the EGRB. Considering that gamma-ray emission comes mostly from jets of blazars and that the jet emission decreases rapidly with increasing jet to line-of-sight angle, it is not surprising that EGRET was not able to detect many large inclination angle active galactic nuclei (AGNs). Though Fermi could only detect a few large inclination angle AGNs during the first three months of its survey, it is expected to detect many such sources in the near future. Since non-blazar AGNs are expected to have higher density as compared to blazars, these could also contribute significantly to the EGRB. In this paper, we discuss contributions from unresolved discrete sources including normal galaxies, starburst galaxies, blazars and off-axis AGNs to the EGRB.

A Joint Source-Channel Coding Scheme for Transmission of Correlated Discrete Sources over a Gaussian Multiple Access Channel

We consider the problem of transmission of correlated discrete alphabet sources over a Gaussian Multiple Access Channel (GMAC). A distributed bit-to-Gaussian mapping is proposed which yields jointly Gaussian codewords. This can guarantee lossless transmission or lossy transmission with given distortions, if possible. The technique can be extended to the system with side information at the encoders and decoder.