Abstract:
Aim. To determine the antimicrobial potential of guava (Psidium guajava) leaf extracts against two gram-negative bacteria (Escherichia coli and Salmonella enteritidis) and two gram-positive bacteria (Staphylococcus aureus and Bacillus cereus) which are some of foodborne and spoilage bacteria. The guava leaves were extracted in four different solvents of increasing polarities (hexane, methanol, ethanol, and water). The efficacy of these extracts was tested against those bacteria through a well-diffusion method employing 50？μL leaf-extract solution per well. According to the findings of the antibacterial assay, the methanol and ethanol extracts of the guava leaves showed inhibitory activity against gram-positive bacteria, whereas the gram-negative bacteria were resistant to all the solvent extracts. The methanol extract had an antibacterial activity with mean zones of inhibition of 8.27 and 12.3？mm, and the ethanol extract had a mean zone of inhibition of 6.11 and 11.0？mm against B. cereus and S. aureus, respectively. On the basis of the present finding, guava leaf-extract might be a good candidate in the search for a natural antimicrobial agent. This study provides scientific understanding to further determine the antimicrobial values and investigate other pharmacological properties. 1. Introduction Recently there has been a lot of attention focused on producing medicines and products that are natural. Several fruits and fruit extracts, as well as arrowroot tea extract [1] and caffeine [2], have been found to exhibit antimicrobial activity against E. coli O157:H7. This suggests that plants which manifest relatively high levels of antimicrobial action may be sources of compounds that can be used to inhibit the growth of foodborne pathogens. Bacterial cells could be killed by the rupture of cell walls and membranes and by the irregular disruption of the intracellular matrix when treated with plant extracts [1]. The guava (Psidium guajava) is a phytotherapic plant used in folk medicine that is believed to have active components that help to treat and manage various diseases. The many parts of the plant have been used in traditional medicine to manage conditions like malaria, gastroenteritis, vomiting, diarrhea, dysentery, wounds, ulcers, toothache, coughs, sore throat, inflamed gums, and a number of other conditions [3–5]. This plant has also been used for the controlling of life-changing conditions such as diabetes, hypertension, and obesity [3, 6–10]. In this study, we aim to evaluate the total extracts of P. guajava leaves, growing at Fort Valley State

Abstract:
We study different properties of convergent, null, and bounded double sequence spaces of fuzzy real numbers like completeness, solidness, sequence algebra, symmetricity, convergence-free, and so forth. We prove some inclusion results too. 1. Introduction Throughout the paper, a double sequence is denoted by , a double infinite array of elements , where each is a fuzzy real number. The initial work on double sequences is found in Bromwich [1]. Later on, it was studied by Hardy [2], Móricz [3], Tripathy [4], Basarir and Sonalcan [5], and many others. Hardy [2] introduced the notion of regular convergence for double sequences. The concept of paranormed sequences was studied by Nakano [6] and Simons [7] at the initial stage. Later on, it was studied by many others. After the introduction of fuzzy real numbers, different classes of sequences of fuzzy real numbers were introduced and studied by Tripathy and Nanda [8], Choudhary and Tripathy [9], Tripathy et al. [10–13], Tripathy and Dutta [14–16], Tripathy and Borgogain [17], Tripathy and Das [18], and many others. Let denote the set of all closed and bounded intervals on , the real line. For , , we define where and . It is known that ？？is a complete metric space. A fuzzy real number is a fuzzy set on , that is, a mapping associating each real number with its grade of membership . The -level set of the fuzzy real number , for , is defined as . The set of all upper semicontinuous, normal, and convex fuzzy real numbers is denoted by , and throughout the paper, by a fuzzy real number, we mean that the number belongs to . Let , and let the -level sets be ; the product of and is defined by 2. Definitions and Preliminaries A fuzzy real number is called convex if , where . If there exists such that , then the fuzzy real number is called normal. A fuzzy real number is said to be upper semicontinuous if, for each , , for all , is open in the usual topology of . The set of all real numbers can be embedded in . For , is defined by The absolute value, of , is defined by (see, e.g., [19]) A fuzzy real number is called nonnegative if , for all . The set of all nonnegative fuzzy real numbers is denoted by . Let be defined by Then defines a metric on . The additive identity and multiplicative identity in are denoted by , respectively. A sequence of fuzzy real numbers is said to be convergent to the fuzzy real number if, for every , there exists such that , for all . A sequence of fuzzy numbers converges to a fuzzy number if both and hold for every [20]. A sequence of generalized fuzzy numbers converges weakly to a

Abstract:
The $C^*$-algebra of continuous functions on the quantum quaternion sphere $H_q^{2n}$ can be identified with the quotient algebra $C(SP_q(2n)/SP_q(2n-2))$. In commutative case i.e. for $q=1$, the topological space $SP(2n)/SP(2n-2)$ is homeomorphic to the odd dimensional sphere $S^{4n-1}$. In this paper, we prove the noncommutative analogue of this result. Using homogeneous $C^*$-extension theory, we prove that the $C^*$-algebra $C(H_q^{2n})$ is isomorphic to the $C^*$-algebra $C(S_q^{4n-1})$. This further implies that for different values of $q \in [0,1)$, the $C^*$-algebras underlying the noncommutative space $H_q^{2n}$ are isomorphic.

Abstract:
We give an explicit description of the $q$-deformation of symplectic group $SP_{q}(2n)$ at the $C^*$-algebra level and find all irreducible representations of this $C^{*}$-algebra. Further we describe the $C^*$-algebra of the quotient space $SP_{q}(2n)/SP_{q}(2n-2)$ in terms of generators and relations. We compute its $K$-theory by obtaining a chain of short exact sequence for the $C^{*}$-algebras underlying such manifolds.

Aromatic systems like phenol, diphenol, cyano benzene, chloro benzene, aniline
etc shows effective π-π stacking interactions, long range van der Waals
forces; ion-π interactions etc. and these forces of interactions play an crucial
role in the stability of stacked π-dimeric system. On the other hand, substituents
and conformational change in the stacked dimmers of aromatic system
may also change the stability of different stacked dimers. In this current
study, stacked phenolic dimmers (both phenol and diphenol) have been taken
for investigation of the stacking π-π interaction. But, the stacking interactions
are also greatly affected by the conformational change with internal rotation
(i.e. dihedral angle, φ) between the stacked dimers. It is generally accepted
that larger basis sets are required for the highly accurate calculation of interaction
energies for any stacked aromatic models. But, it has recently been reported
that M062X/6-311++G(d,p) basis set is effectively better than that of
B3LYP/6-311++G(d,p) for determining the interaction energies for any kind
of long range interaction in aromatic systems. Therefore, all the calculations
were carried out by using M062X/6-311++G(d,p) basis set. However, in most
of the cases the calculated π-π stacking interaction energies show almost same
result for both DFT and ab initio methods.

Abstract:
Agricultural regionalization is basically depends on cropping intensity and combination. The crops are generally grown in combination with other crops (Ramasundaram et. all 2012). Empirical analysis of crop combinations, ranking and agricultural efficiency can be the basis of delineation of agricultural regions in micro and macro level. Agriculture is the backbone of the economy of the district of Jalpaiguri and the land use pattern quite differs from that of West Bengal due to its diversity in relief and climate. Attempts have been made in this paper to show agricultural regions of Jalpaiguri district within its 13 blocks by the statistical techniques

Abstract:
We employ Ramanujan's formula to prove three conjectures of R. S. Melham on representation of an integer as sums of polygonal numbers. 1. Introduction Jacobi’s classical two-square theorem is as follows. Theorem 1 (see [1]). Let denote the number of representations of as a sum of two squares, counting order and sign, and let denote the number of positive divisors of congruent to modulo . Then The above theorem can also be recasted in terms of Lambert series as Similar representation theorems involving squares and triangular numbers were found by Dirichlet [2], Lorenz [3], Legendre [4], and Berndt [5]. For example, the following two theorems are due to Lorenz and Ramanujan, respectively. Theorem 2 (see [3]). Let denote the number of representations of as a sum of times a square and times a square. Then Theorem 3 (see [5]). Let denote the number of representations of as a sum of times a triangular number and times a triangular number. Then Hirschhorn [6, 7] obtained forty-five similar identities (including those obtained by Legendre and Ramanujan) involving squares, triangular numbers, pentagonal numbers, and octagonal numbers employing dissection of the -series representations of the identities obtained by Jacobi, Dirichlet, and Lorenz. In [8], Baruah and the author obtained twenty-five more such identities involving squares, triangular numbers, pentagonal numbers, heptagonal numbers, octagonal numbers, decagonal numbers, hendecagonal numbers, dodecagonal numbers, and octadecagonal numbers. More works on this topic have been done in [9–11]. In [11], Melham presented 21 conjectured analogues of Jacobi’s two-square theorem which are verified using computer algorithms. In [12], Toh offered a uniform approach to prove these conjectures using known formulae for . In this paper, we show that some of these conjectures can also be proved by using Ramanujan’s famous formula. We prove three conjectures enlisted in the following theorem which have appeared as , , and , respectively, in [11]. Theorem 4. Consider The next section of this paper is devoted to notations, definitions, and preliminary results. 2. Notations and Preliminary Results Ramanujan’s general theta-function is defined by [5, page 34, (18.1)] Jacobi’s famous triple product identity takes the simple form [5, page 35, Entry 19] where, here and throughout the paper, for , We also use the following notation for the sake of brevity of expressions: One important special case of is where the product representations in (12) arise from (9). From [5, page 46, Entry 30] we find that Also if , then [5, page 45,

An exact scalar field cosmological model is constructed from the
exact solution of the field equations. The solutions are exact and no
approximation like slow roll is used. The model gives inflation, solves horizon
and flatness problems. The model also gives a satisfactory estimate of present
vacuum energy density as well as vacuum energy density at Planck epoch and
solves cosmological constant problem of 120 orders of magnitude discrepancy of
vacuum energy density. Further, this model predicts existence of dark
matter/energy and gives an extremely accurate estimate of present energy
density of dark matter and energy. Along with explanations of graceful exit, radiation
era, matter domination, this model also indicates the reason for present
accelerated state of the universe. In this work a method is shown following
which one can construct an infinite number of exact scalar field inflationary
cosmological models.

Abstract:
The
modified Emden-type is being investigated by mathematicians as well as
physicists for about a century. However, there exist no exact explicit solution
of this equation, ẍ + αxẋ + βx^{3} = 0for arbitrary values of α and β. In this work,
the exact analytical explicit solution of modified Emden-type (MEE) equation is
derived for arbitrary values of α and β. The Lagrangian and Hamiltonian of
MEE are also
worked out. The solution is also utilized to find exact explicit analytical
solution of Force-free Duffing oscillator-type equation. And exact explicit
analytical solution of two-dimensional Lotka-Volterra System is
also worked out.

Abstract:
The purpose of this study is to explore the possible applicability of Sterculia urens gum as a novel carrier for colonic delivery system of a sparingly soluble drug, azathioprine. The study involves designing a microflora triggered colon-targeted drug delivery system (MCDDS) which consists of a central polysaccharide core and is coated to different film thicknesses with blends of chitosan/Eudragit RLPO, and is overcoated with Eudragit L00 to provide acid and intestinal resistance. The microflora degradation property of gum was investigated in rat caecal medium. Drug release study in simulated colonic fluid revealed that swelling force of the gum could concurrently drive the drug out of the polysaccharide core due to the rupture of the chitosan/Eudargit coating in microflora-activated environment. Chitosan in the mixed film coat was found to be degraded by enzymatic action of the microflora in the colon. Release kinetic data revealed that the optimized MCDDS was fitted well into first-order model, and apparent lag time was found to be 6 hours, followed by Higuchi release kinetics. In vivo study in rabbits shows delayed , prolonged absorption time, decreased , and absorption rate constant (Ka), indicating a reduced systemic toxicity of the drug as compared to other dosage forms. 1. Introduction In the recent times, colon-specific technologies have utilized single or combination of the following primary approaches, with varying degrees of success: (1) pH-dependent systems, (2) time-dependent systems, (3) prodrugs, and (4) colonic microflora-activated systems [1, 2]. Among the different approaches to achieve colon specific drug delivery system, the use of polymers specifically degraded by colonic bacterial enzymes (such as β-glucoronidase, β-xylosidase, β-galactosidase, and azoreductase) holds promise. Microbially activated delivery systems for colon targeting are being developed to exploit the potential of the specific nature of diverse and luxuriant microbiota associated with the colon compared to other parts of the gastrointestinal (GI) tract. These colonic microbiotas produce a large number of hydrolytic and reductive enzymes which can potentially be utilized for colonic delivery [1, 2]. Most of these systems are based on the fact that anaerobic bacteria in the colon are able to recognize the various substrates and degrade them with their enzymes. Natural gums are often preferred to synthetic materials due to their low-toxicity, low-cost, and easy availability. A number of colon-targeted delivery systems based both on combination of pH, polysaccharides