Associated Lam\'{E} Equation, Periodic Potentials and sl(2,R)

We propose a new approach based on the algebraization of the Associated Lam\'{e} equation $$-\psi''(x) + [ m(m+1)k^{2}sn^{2}x + \ell(\ell+1)k^{2}(cn^{2}x/dn^{2}x)]\psi(x) = E\psi(x)$$ within sl(2,R) to derive the corresponding periodic potentials. The band edge eigenfunctions and energy spectra are explicitly obtained for integers m,$\ell$. We also obtain the explicit expressions of the solutions for half-integer m and integer or half-integer $\ell$.Comment: 8 pages, no figure, tex file(version 2.09

The Fe2(+)-Mg interdiffusion in orthopyroxene: Constraints from cation ordering and structural data and implications for cooling rates of meteorites

Orthopyroxene crystals in a number of meteorites exhibit compositional zoning of Fe and Mg, which provide important constraint on their cooling rates. However, attempts to model cooling rate of these crystals from Fe-Mg zoning profiles suffer from the lack of any measured or theoretically well constrained Fe-Mg interdiffusion data in OP(x) It has been assumed that Fe-Mg interdiffusion in OP(x) only slightly slower than that in olivine. The purpose of this paper is to (1) calculate the Fe-Mg fractionation, and (2) provide analytical formulation relating cooling rate to the length of the diffusion zone across the interface of the overgrowth of a mineral on itself with application to Mg diffusion profile across OP(x) growth on OP(x) in certain mesosiderites

Utilization of mouldy sorghum and Cassia tora through fermentation for feed purposes

Microbial fermentation of mouldy grains brought about by lactic acid bacteria is gaining much significance owing to their ability to inhibit mould growth and detoxify mycotoxins while improving the nutritive value and safety of the product. In the present study the potential of developing a probiotic feed ingredient from a combination of mouldy sorghum and Cassia tora seeds, using spontaneous fermentation was explored. The effect of fermentation at 0, 24 and 36 h on the microflora, ergosterol,mycotoxins and nutritive value, of mouldy sorghum was assessed individually and in combination with C. tora seeds. A reduction in mould counts upto 58 and 96% was observed at 24 and 36 h of fermentingmouldy sorghum. Total plate count increased by 2 fold and Lactobacillus count increased by 4 fold when mouldy sorghum was fermented singly or with C. tora seeds. Fermentation decreased ergosterol by 76%,aflatoxin to non-detectable levels at 36 h of fermentation and fumonisin B1 to non-detectable levels at 24 and 36 h of fermentation of mouldy sorghum. Fermentation resulted in marginal improvement in nutritivevalue of mouldy sorghum when estimated in terms of proximate principles and mineral elements. Addition of C. tora resulted in considerable increase in nutritive value particularly with respect to protein and mineral elements like iron and calcium in mouldy sorghum

pBWT: Achieving succinct data structures for parameterized pattern matching and related problems

The fields of succinct data structures and compressed text indexing have seen quite a bit of progress over the last two decades. An important achievement, primarily using techniques based on the Burrows-Wheeler Transform (BWT), was obtaining the full functionality of the suffix tree in the optimal number of bits. A crucial property that allows the use of BWT for designing compressed indexes is order-preserving suffix links. Specifically, the relative order between two suffixes in the subtree of an internal node is same as that of the suffixes obtained by truncating the furst character of the two suffixes. Unfortunately, in many variants of the text-indexing problem, for e.g., parameterized pattern matching, 2D pattern matching, and order-isomorphic pattern matching, this property does not hold. Consequently, the compressed indexes based on BWT do not directly apply. Furthermore, a compressed index for any of these variants has been elusive throughout the advancement of the field of succinct data structures. We achieve a positive breakthrough on one such problem, namely the Parameterized Pattern Matching problem. Let T be a text that contains n characters from an alphabet , which is the union of two disjoint sets: containing static characters (s-characters) and containing parameterized characters (p-characters). A pattern P (also over ) matches an equal-length substring S of T i the s-characters match exactly, and there exists a one-to-one function that renames the p-characters in S to that in P. The task is to find the starting positions (occurrences) of all such substrings S. Previous index [Baker, STOC 1993], known as Parameterized Suffix Tree, requires (n log n) bits of space, and can find all occ occurrences in time O(jPj log +occ), where = jj. We introduce an n log +O(n)-bit index with O(jPj log +occlog n log ) query time. At the core, lies a new BWT-like transform, which we call the Parame- terized Burrows-Wheeler Transform (pBWT). The techniques are extended to obtain a succinct index for the Parameterized Dictionary Matching problem of Idury and Schaer [CPM, 1994]

Structural Pattern Matching - Succinctly

Let T be a text of length n containing characters from an alphabet Sigma, which is the union of two disjoint sets: Sigma_s containing static characters (s-characters) and Sigma_p containing parameterized characters (p-characters). Each character in Sigma_p has an associated complementary character from Sigma_p. A pattern P (also over Sigma) matches an equal-length substring $S$ of T iff the s-characters match exactly, there exists a one-to-one function that renames the p-characters in S to the p-characters in P, and if a p-character x is renamed to another p-character y then the complement of x is renamed to the complement of y. The task is to find the starting positions (occurrences) of all such substrings S. Previous indexing solution [Shibuya, SWAT 2000], known as Structural Suffix Tree, requires Theta(nlog n) bits of space, and can find all occ occurrences in time O(|P|log sigma+ occ), where sigma = |Sigma|. In this paper, we present the first succinct index for this problem, which occupies n log sigma + O(n) bits and offers O(|P|logsigma+ occcdot log n logsigma) query time

Unveiling Microlensing Biases in Testing General Relativity with Gravitational Waves

Gravitational waves (GW) from chirping binary black holes (BBHs) provide unique opportunities to test general relativity (GR) in the strong-field regime. However, testing GR can be challenging when incomplete physical modeling of the expected signal gives rise to systematic biases. In this study, we investigate the potential influence of wave effects in gravitational lensing (which we refer to as microlensing) on tests of GR using GWs for the first time. We utilize an isolated point-lens model for microlensing with the lens mass ranging from $10-10^5~$M$_\odot$ and base our conclusions on an astrophysically motivated population of BBHs in the LIGO-Virgo detector network. Our analysis centers on two theory-agnostic tests of gravity: the inspiral-merger-ringdown consistency test (IMRCT) and the parameterized tests. Our findings reveal two key insights: First, microlensing can significantly bias GR tests, with a confidence level exceeding $5\sigma$. Notably, substantial deviations from GR $(\sigma > 3)$ tend to align with a strong preference for microlensing over an unlensed signal, underscoring the need for microlensing analysis before claiming any erroneous GR deviations. Nonetheless, we do encounter scenarios where deviations from GR remain significant ($1 < \sigma < 3$), yet the Bayes factor lacks the strength to confidently assert microlensing. Second, deviations from GR correlate with pronounced interference effects, which appear when the GW frequency ($f_\mathrm{GW}$) aligns with the inverse time delay between microlens-induced images ($t_\mathrm{d}$). These false deviations peak in the wave-dominated region and fade where $f_\mathrm{GW}\cdot t_\mathrm{d}$ significantly deviates from unity. Our findings apply broadly to any microlensing scenario, extending beyond specific models and parameter spaces, as we relate the observed biases to the fundamental characteristics of lensing.Comment: 21 pages, 12 figure

Nonsingular potentials from excited state factorization of a quantum system with position dependent mass

The modified factorization technique of a quantum system characterized by position-dependent mass Hamiltonian is presented. It has been shown that the singular superpotential defined in terms of a mass function and a excited state wave function of a given position-dependent mass Hamiltonian can be used to construct non-singular isospectral Hamiltonians. The method has been illustrated with the help of a few examples.Comment: Improved version accepted in J. Phys.