Abstract:
Shannon in his 1949 paper suggested the use of derivatives to increase the W*T product of the sampled signal. Use of derivatives enables improved reconstruction particularly in the case of non-uniformly sampled signals. An FM-AM representation for Lagrange/Hermite type interpolation and a reconstruction technique are discussed. The representation using a product of a polynomial and exponential of a polynomial is extensible to two dimensions. When the directly available information is inadequate, estimation of the signal and its derivative based on the correlation characteristics of Gaussian filtered noise has been studied. This requires computation of incomplete normal integrals. Reduction methods for reducing multivariate normal variables include multistage partitioning, dynamic path integral and Hermite expansion for computing the probability integrals necessary for estimating the mean of the signal and its derivative at points intermediate between zero or threshold crossings. The signals and their derivatives as measured or estimated are utilized to reconstruct the signal at a desired sampling rate.

Abstract:
The Teager-Kaiser energy operator (TKO) belongs to a class of autocorrelators and their linear combination that can track the instantaneous energy of a nonstationary sinusoidal signal source. TKO-based monocomponent AM-FM demodulation algorithms work under the basic assumption that the operator outputs are always positive. In the absence of noise, this is assured for pure sinusoidal inputs and the instantaneous property is also guaranteed. Noise invalidates both of these, particularly under small signal conditions. Post-detection filtering and thresholding are of use to reestablish these at the cost of some time to acquire. Key questions are: (a) how many samples must one use and (b) how much noise power at the detector input can one tolerate. Results of study of the role of delay and the limits imposed by additive Gaussian noise are presented along with the computation of the cumulants and probability density functions of the individual quadratic forms and their ratios.

Abstract:
Objective: The World health organization (WHO) has accepted Keith Edward scoring system for the diagnosis of childhood tuberculosis (TB). In the present study, we evaluated this scoring system. Methods and Results: We included 53 children with confirmed TB involving different organs, admitted in NB Medical College, during two years period as cases; and 50 randomly selected, age, sex, and organ matched confirmed non-TB cases as controls. We noticed 15.1% false negative and 22% false positive results in our study, and the scoring system had 84.9% sensitivity, 78% specificity, and 80.36% positive predictive value. Likelihood ratio positive (LR+) was 3.86, likelihood ratio negative (LR-) was 0.19, and overall agreement was 81.55%. We observed that Keith Edward scoring system was less effective in children suffering from non-TB chronic diseases (false positive rate: 45.5%). We found no significant difference in nutritional status between study and control groups (P = 0.65). We noticed that more than 15-mm indurations for tuberculin test were specific for TB in children. Conclusion: We concluded that Keith Edward scoring system is good for public health purpose, but there is a scope for improvement, and further study is required for this purpose.

Temperature dependence of diquark mass has been investigated in the
framework of the quasi particle diquark model. The effective mass of the
diquark has been suggested to have a temperature dependence which shows a power
law behavior. The variation of the diquark mass with temperature has been
studied. A decrease in effective mass at temperature T < T_{c},
where T_{c}is the critical
temperature has been observed. Some features of the phase transition have been
discussed. The phase transition is found to be of second order. Temperature
variation of baryon masses has also been studied. The results are compared and
discussed with available works.

Abstract:
A class of transformations of $R_q$-matrices is introduced such that the $q\to 1$ limit gives explicit nonstandard $R_{h}$-matrices. The transformation matrix is singular itself at $q\to 1$ limit. For the transformed matrix, the singularities, however, cancel yielding a well-defined construction. Our method can be implemented systematically for R-matrices of all dimensions and not only for $sl(2)$ but also for algebras of higher dimensions. Explicit constructions are presented starting with ${\cal U}_q(sl(2))$ and ${\cal U}_q(sl(3))$, while choosing $R_q$ for (fund. rep.)$\otimes$(arbitrary irrep.). The treatment for the general case and various perspectives are indicated. Our method yields nonstandard deformations along with a nonlinear map of the $h$-Borel subalgebra on the corresponding classical Borel subalgebra. For ${\cal U}_h(sl(2))$ this map is extended to the whole algebra and compared with another one proposed by us previously.

Abstract:
The generators $(J_{\pm}, J_0)$ of the algebra $U_q(sl(2))$ is our starting point. An invertible nonlinear map involving, apart from q, a second arbitrary complex parameter h, defines a triplet $({\hat X},{\hat Y},{\hat H})$. The latter set forms a closed algebra under commutation relations. The nonlinear algebra $U_{q,h}(sl(2))$, thus generated, has two different limits. For $q \to 1$, the Jordanian h-deformation $U_{h}(sl(2))$ is obtained. For $h \to 0$, the q-deformed algebra $U_{q}(sl(2))$ is reproduced. From the nonlinear map, the irreducible representations of the doubly-deformed algebra $U_{q,h}(sl(2))$ may be directly and explicitly obtained form the known representations of the algebra $U_q(sl(2))$. Here we consider only generic values of q.

Abstract:
Using the contraction procedure introduced by us in Ref. \cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra ${\cal U}_{\sf h}(sl(3))$ which has a remarkably simple coalgebraic structure and contains the Jordanian Hopf algebra ${\cal U}_{\sf h}(sl(2))$, obtained by Ohn, as a subalgebra. A nonlinear map between ${\cal U}_{\sf h}(sl(3))$ and the classical $sl(3)$ algebra is then established. In the second part, we give the higher dimensional Jordanian algebras ${\cal U}_{\sf h}(sl(N))$ for all $N$. The Universal ${\cal R}_{\sf h}$-matrix of ${\cal U}_{\sf h} (sl(N))$ is also given.

Abstract:
The generators of the Jordanian quantum algebra ${\cal U}_h(sl(2))$ are expressed as nonlinear invertible functions of the classical $sl(2)$ generators. This permits immediate explicit construction of the finite dimensional irreducible representations of the algebra ${\cal U}_h(sl(2))$. Using this construction, new finite dimensional solutions of the Yang-Baxter equation may be obtained.

Abstract:
By solving a set of recursion relations for the matrix elements of the ${\cal U}_h(sl(2))$ generators, the finite dimensional highest weight representations of the algebra were obtained as factor representations. Taking a nonlinear combination of the generators of the two copies of the ${\cal U}_h(sl(2))$ algebra, we obtained ${\cal U}_h(so(4))$ algebra. The latter, on contraction, yields ${\cal U}_h(e(3))$ algebra. A nonlinear map of ${\cal U}_h(e(3))$ algebra on its classical analogue $e(3)$ was obtained. The inverse mapping was found to be singular. It signifies a physically interesting situation, where in the momentum basis, a restricted domain of the eigenvalues of the classical operators is mapped on the whole real domain of the eigenvalues of the deformed operators.

Abstract:
For a class of multiparameter statistical models based on 2×2 braid matrices, the eigenvalues of the transfer matrix () are obtained explicitly for all (,). Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out, and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of () matrices. The role of free parameters, increasing as 2 with N, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for all N. Inverse Cayley transforms of the Yang-Baxter matrices corresponding to our braid matrices are obtained for all N. They provide potentials for factorizable S-matrices. Main results are summarized, and perspectives are indicated in the concluding remarks.