Mumtaz Ahmad Khan

PROTEOLYTIC ACTIVITY IN THE DIGESTIVE TRACT OF THE WATER SCORPION LACCOTREPHIS MACULATUS FABR., (NEPIDAE: HEMIPTERA)

An attempt has been made to investigate the activity of different proteolytic enzymes in the extract of the digestive tract of Laccotrephis maculatus which is predatory in habit. A pepsin‐like activity is absent. But, however, the proteolytic activity in the extracts occurs between pH range 4.0 to 10.0 and there are two peaks of activity, one occurring at pH 5.0 and the other at pH 8.5. These activities respectively correspond to catheptic and tryptic activities occurring in the digestive tract of mammals.

On some properties of the generalized Mittag-Leffler function

This paper deals with the study of a generalized function of Mittag-Leffler type. Various properties including usual differentiation and integration, Euler(Beta) transforms, Laplace transforms, Whittaker transforms, generalized hypergeometric series form with their several special cases are obtained and relationship with Wright hypergeometric function and Laguerre polynomials is also established.2000 Mathematics Subject Classification33C45, 47G20, 26A33.

Effect of triol and makisterone A on the haemocytes ofHieroglyphus nigrorepletus Bolivar (Orthoptera: Acrididae)

Fifth instar hoppers (48 h old) ofHieroglyphus nigrorepletus were injected with different sub-lethal doses (0·5, 1, 2, 4 and 6 μg/hopper) of triol — and makisterone A, after 3 days the haemocytes of these hoppers were selectively damaged. The granular haemocytes, being the most susceptible cells were completely damaged even by the weakest dose of triol and makisterone A. Prohaemocytes and plasmatocytes were intensely damaged by 1 μg of makisterone A, 2 and 1 μg doses of triol respectively. However, oenocytoids were comparatively resistant cells, but they were also damaged by 2 μg triol and 4 μg makisterone A. Following the emergence of adults from the treated hoppers after 3 days, both granular haemocytes and plasmatocytes were indistinguishable with respect to even weakest dose of both the hormones. Comparatively prohaemocytes were less damaged and could be recognized in adults affected with 1 and 2 μg of makisterone A and triol respectively. However, oenocytoids were completely disintegrated in adults emerged from the hoppers injected with 1 and 2 μg of triol and makisterone A respectively. In adults of both sexes, respective haemocytes developed almost similar pathological condition with regard to each dose.

Some Umbral Calculus Presentations of the Chan-Chyan-Srivastava Polynomials and the Erkuș-Srivastava Polynomials

In their recent investigation involving differential operators for the generalized Lagrange polynomials, Chan et. al. [3] encountered and proved a certain summation identity and several other results for the Lagrange polynomials in several variables, which are popularly known in the literature as the Chan-Chyan-Srivastava polynomials. These multivariable polynomials have been studied systematically and extensively in the literature ever since then (see, for example, [1], [4], [9], [11], [12] and [13]). In the present paper, we investigate umbral calculus presentations ofthe Chan-Chyan-Srivastava polynomials and also of their substantially more general form, the Erkus-Srivastava polynomials [9]. Some other closely-related results are also considered.

On Some Properties of a Generalization of Bessel-Maitland Function

The present paper is the investigation of certain properties of generalized Bessel-Maitland function, written in the form ࡶ ࣇ ,ࢗ ࣆ ,ࢽ (ࢠ ) = ∑ � ஶ ࢔ୀ૙ (ࢽ )ࢗ࢔ (ࢠ )࢔ ࢔ !ડ (ࣆ࢔ ାࣇା૚ ) , where ࣆ ,ࣇ ,ࢽ∈ ࡯ ;ࡾࢋ (ࣆ ) ≥ ૙ , ࡾࢋ (ࣇ ) ≥ −૚ ,ࡾࢋ (ࢽ ) ≥ ૙ and ࢗ∈ (૙ ,૚ )∪ ࡺ. For the function ࡶ ࣇ ,ࢗ ࣆ ,ࢽ (ࢠ ) , a number of results including differentiation and integration formulas, Mellin-Barnes integral representation, Laplace transform, Euler transform, ࢑ -transform, Varma transform, Mellin transform. Various relationship with other functions including Foxs ࡴ-function and Wright hypergeometric function were also established. In the end certain relations have been obtained by using the Riemann-Liouville fractional integrals and derivatives.

On some generalized Sister Celine's polynomials

Certain generalizations of Sister Celines polynomials are given which include most of the known polynomials as their special cases. Besides, generating functions and integral representations of these generalized polynomials are derived and a relation between generalized Laguerre polynomials and generalized Batemans polynomials is established.

Phospholipid concentration in the fat body and gonads of red cotton bug, Dysdercus cingulatus Fabr. (Heteroptera: Pyrrhocoridae) in relation to growth, metamorphosis and reproduction.

Abstract In Dysdercus cingulatus the phospholipid concentration in the fat body of the fifth instar nymphs rises after moulting and reaches to a peak level in the intermoult period. But this level falls prior to metamorphosis. After emerging as adults both sexes show almost parallel changes in phospholipid levels in the fat body and gonads up to ten days, which include two reproductive cycles. Although the tissues of the females have higher phospholipid levels than those of the males of corresponding age, the concentration for both sexes is invariably lower in the fat body than in the gonads. The initial increase in phospholipid concentration in the fat body and in the gonadal tissues following emergence is related to the maturation of the adults.

EULER TYPE INTEGRAL INVOLVING GENERALIZED MITTAG-LEFFLER FUNCTION

Abstract. In this paper, we obtain some theorems on certain Euler typeintegrals involving generalized Mittag-Leffler function. Further, we de-duce some special cases involving Wiman function, Prabhakar functionand exponential and binomial functions. 1. IntroductionIn 1903, the Swedish mathematician Gosta Mittag-Leffler [6] introduced thefunction(1.1) E α (z) =X ∞n=0 z n Γ(αn +1), α ∈ C, Re(α) > 0,where z is a complex variable and α ≥ 0. The Mittag-Leffler function is a di-rect generalization of exponential function to which it reduces for α = 1. For0 < α < 1 it interpolates between the pure exponential and hypergeometricfunction 11−z . Its importance is realized during the last two decades due toits involvement in the problems of physics, chemistry, biology, engineering andapplied sciences. Mittag-Leffler function naturally occurs as the solution offractional order differential or fractional order integral equation. The general-ization of E α (z) was studied by Wiman [11] in 1905 and he defined the functionas(1.2) E

On binomial operator representations of certain polynomial

Based on the technique used by M.A.Khanand A. K. Shukla [4] here finite series representations of binomial partial differential operators have been used to establish operator representations of various polynomials not considered in the earlier mentioned paper. The results obtained are believed to be new.

Application of Z-transform on a new polynomial set

Abstract. The present paper deals with a new polynomial set and the application of the -transform on it.