Derivation of the solution of certain singular integral equations

It is shown that the a;P?lication of the Poincare-Bertrand fcm~ulaw hen made in a suitable manner produces the s~lutiano f certain singular integral equations very quickly, thc method of arriving at which, otherwise, is too complicaled. Two singular integral equations are considered. One of these quaiions is with a Cauchy-tyge kcrnel arid the other is an equalion which appears in the a a w guide theory and the theory of dishcations. Adifferent approach i? alw made here to solve the singular integralquation> of the waveguide theor? ind this i ~ v o l v eth~e use of the inversion formula of the Cauchy-type singular integral equahn and dudion to a system of TIilberl problems for two unknowns which can be dwupled wry easily to obi& tbe closed form solutim of the irilegral equatlou at band. The methods of the prescnt paper avoid all the complicaled approaches of solving the singular integral equaticn of the waveguide theory knowr todate.

Derivation of the decoupling relations for composite models from anomaly constraints and n-independence

It is shown, in the composite fermion models studied by 't Hooft and others, that the requirements of Adler-Bell-Jackiw anomaly matching and n-independence are sufficient to fix the indices of composite representations. The third requirement, namely that of decoupling relations, follows from these two constraints in such models and hence is inessential.

On the axiomatic approach to the maximum entropy principle of inference

Recent axiomatic derivations of the maximum entropy principle from consistency conditions are critically examined. We show that proper application of consistency conditions alone allows a wider class of functionals, essentially of the form ∝ dx p(x)[p(x)/g(x)] s , for some real numbers, to be used for inductive inference and the commonly used form − ∝ dx p(x)ln[p(x)/g(x)] is only a particular case. The role of the prior densityg(x) is clarified. It is possible to regard it as a geometric factor, describing the coordinate system used and it does not represent information of the same kind as obtained by measurements on the system in the form of expectation values.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

Adsorption of Nitrogen on Activated Carbon-Refit of Experimental Data and Derivation of Properties Required for Design of Equipment

Volumetric method based adsorption measurements of nitrogen on two specimens of activated carbon (Fluka and Sarabhai) reported by us are refitted to two popular isotherms, namely, Dubunin−Astakhov (D−A) and Toth, in light of improved fitting methods derived recently. Those isotherms have been used to derive other data of relevance in design of engineering equipment such as the concentration dependence of heat of adsorption and Henry’s law coefficients. The present fits provide a better representation of experimental measurements than before because the temperature dependence of adsorbed phase volume and structural heterogeneity of micropore distribution have been accounted for in the D−A equation. A new correlation to the Toth equation is a further contribution. The heat of adsorption in the limiting uptake condition is correlated with the Henry’s law coefficients at the near zero uptake condition.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Path-integral derivation of the superconformal anomaly for the Wess-Zumino model

Fujikawa's method of evaluating the anomalies is extended to the on-shell supersymmetric (SUSY) theories. The supercurrent and the superconformal current anomalies are evaluated for the Wess-Zumino model using the background-field formulation and heat-kernel regularization. We find that the regularized Jacobians for SUSY and superconformal transformations are finite. The results can be expressed in a form such that there is no supercurrent anomaly but a finite nonzero superconformal anomaly, in agreement with similar results obtained using other methods.

Principle of a Dual Current Source Converter for AC Motor Drives

The principle of operation of a dual current source converter is briefly explained. The combination of two single current source converters (SCSC) to form a ``dual (duplex) current source converter'' (DCSC) is proposed. The DCSC is shown to have the following merits: 1) it retains all the advantages of the SCSC; 2) it reduces the harmonic content of the current waveform considerably; and 3) since the load current is shared equally between two current source converters, ratings of the individual components employed in the circuit are considerably lowered. A DCSC can be an attractive choice for sophisticated large horsepower drives where a good performance of the drive rather than cost is a prime factor. An open-loop control scheme employing the DCSC for an ac motor drive has been successfully implemented in the laboratory. Oscillograms of the improved load current waveforms are shown.

A structural principle for a class of adaptive systems

A feature common to many adaptive systems for identification and control is the adjustment.of gain parameters in a manner ensuring the stability of the overall system. This paper puts forward a principle which assures such a result for arbitrary systems which are linear and time invariant except for the adjustable parameters. The principle only demands that a transfer function be positive real. This transfer function dependent on the structure of the system with respect to the parameters. Several examples from adaptive identification, control and observer schemes are given as illustrations of the conceptual simplification provided by the structural principle.

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f is an element of L-1 (G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

The principle of microscopic reversibility in organic chemistry - a critique

The principle of microscopic reversibility is one of the few generalising principles used in organic chemistry which have their roots in the fundamental laws of thermodynamics. It has, therefore, been highly popular. However, although the principle has some important uses, its general application is not without pitfalls. The principle is easy to misunderstand and to misapply: indeed, some of its formulations are semantically dubious. The principle is most dangerous when used as a charm, for it is more subtle than some of its formulations suggest. But above all, the principle may not be used for deducing or disproving the mechanism of a reaction, except when the mechanism in the reverse direction is known independently. For, such use is, perhaps, the deadliest misapplication.

First-principle description of magnonic PdnFem multilayers

Ab-initio calculations are used to determine the parameters that determine magnonic band structure of PdnFem multilayers (n = 2, m <= 8). We obtain the layer-resolved magnetization, the exchange coupling, and the magnetic anisotropy of the Pd-Fe structures. The Fe moment is 3.0 mu(B) close to the Pd layers and 2.2 mu(B) in the middle of the Fe layers. An intriguing but not usually considered aspect is that the elemental Pd is nonmagnetic, similar to Cu spacer layers in other multilayer systems. This leads to a pre-asymptotic ferromagnetic coupling through the Pd (about 40 mJ/m(2)). Furthermore, the Pd acquires a small moment due to spin polarization by neighboring Fe atoms, which translates into magnetic anisotropy. The anisotropies are large, in the range typical for L1(0) structures, which is beneficial for high-frequency applications. (C) 2011 American Institute of Physics. doi:10.1063/1.3556763]

Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).