Mathematics for physics and physicists

Acta Mathematica Nitriensia, 2015

In calculus lectures and seminars students frequently call for demonstrations of usefulness of a new term or proposition. Tasks about tangent or instantaneous velocity are quite legendary, showing the need for derivatives. Similarly, pictures of inscribed or circumscribed rectangles, leading to the definition of Riemann definite integral, are quite popular. In the submitted contribution we aim to demonstrate the usefulness of infinite functional series (power, Taylor), which come in useful for common calculations in physics, and also for formulation of new discoveries and theories in physics.

arXiv (Cornell University), 2022

Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial differential equations and integration theory and its many and diverse applications in sciences and engineering fields makes it an attractive field of study and research. The purpose of these notes is to introduce the basic ideas and theorems of the subject to students of mathematics, physics, or engineering sciences. Our goal is to illustrate the topics with utmost clarity and accuracy, readily understandable by the students or interested readers. Rather than providing just the outlines or sketches of the proofs, we have actually provided the complete proofs of all theorems. This approach will illuminate the necessary steps taken and the machinery used to complete each proof. The prerequisite for understanding the topics presented is the knowledge of Lebesgue measure and integral. This will provide ample mathematical background for an advanced undergraduate or a graduate student in mathematics. Definition 1.1. The set of all complex numbers of modulus 1 is denoted by T is a compact abelian group with binary operation: complex multiplication and topology: open arcs {e ix : x ∈ (a, b)}. Define the periodic function F(x) on R by where f is a function on T. Let χ be the identity function on T , i.e., χ(e ix ) = e ix , x ∈ R.

2010

In this paper we study the methods of Borel and Nachbin resummation applied to the solution of integral equation with Kernels K(yx) , the resummation of divergent series and the possible application to Hadamard finite-part integral and distribution theory

International journal of pure and applied mathematics, 2013

Mycotoxins are natural, secondary metabolites produced by fungi on agricultural commodities in the field and during storage under a wide range of climatic conditions. The ochratoxin A (OTA) is a nephrotoxic mycotoxin produced by several species of Aspergillus and Penicillium. In this study, the influence of carbon and nitrogen sources on ochratoxigenic Penicillium species was assessed. The ochratoxigenic Penicillium species were isolated from poultry feed samples of Andhra Pradesh, India. The isolated ochratoxigenic Penicillium species were identified, screened and characterised as OTA producers by high performance thin layer chromatography (HPTLC) and confirmed by high performance liquid chromatography (HPLC). This experiment was carried out using Czapak yeast Autolysate (CYA) medium with different carbon (C) and nitrogen (N) sources at pH 6.5 and incubated at 25+ 28C under dark condition. Maximum OTA production was recorded in the presence of D-glucose followed by D-galactose and D-lactose as carbon sources. Similarly, the maximum amount of OTA production was observed in thiourea followed by potassium nitrate as nitrogen source. However, OTA production, final pH of the medium, and mycelial yield and OTA production of both the species of Penicillium varied with C and N present in the medium. The kinetics of the both species of Penicillium was observed for 30 days at an interval of three days. The maximum amount of OTA was detected by 12 and 15 days incubation periods for Penicillium nordicum and Penicillium verrucosum, respectively

The effect of temperature and medium on the aggressive Trichoderma aggressivum f. europaeum isolates mycelium growth was investigated. Two isolates of the species from mushroom-growing houses in Western Europe and 20 isolates from Polish mushroom-growing houses and oyster mushroom cultivations were taken into consideration. Growth of experimental isolates was examined on standard agar medium and on manure medium at 15, 20, 25, 30 and 35°C. The mycelium of the examined isolates grew better on the manure medium than on standard agar medium and the optimum temperature for all the examined isolates was 25 and 30°C.

Inthelastdecademostindustrializedcountrieshaveexperiencedasustainedgrowthofvalue added and employment in service sector. (L. George et. Al. 1999). Traditionally most of discussionofthemanagementofinnovationhasbeenbasedonmanufacturingindustry.This is not surprising because manufacturers have tangible products, the development of which normally follows a well defined process. However, service industry is now of greater importance for instance the contribution of service sector in Indian GDP is 55.2 percent accordingtoUnionBudget2010-11ofwhich5.4percentcomesfrombankingandinsurance In general, high per capita income is associated with high proportion of GDS and GDP coming from insurance sector. Thus higher level of development seems to come with high levelofactivitiesintheinsurancesector.Whenvariouscomponentsoftheinsurancemarket develop, insurance sector takes on a bigger share of the GDS and of the GDP. With the liberalisation and entry of private companies in insurance the Indian insurance sector has started showing signs of significant change. The study "Insurance industry-Challenge, Reforms and Realignment", conducted by Confederation of Indian Industry (CII), also said that the sector regulator also needs to phase in changes based on regulatory impact assessment, thereby giving industry time to adjust to the changed environment, along with initiatives to drive insurance awareness programmes. This paper is primarily concerned of problemsininsurancesector'sinnovationandtheneedtoaccelerateinnovationrate.Wewill alsotrytocomparetherateofinnovationofvariouscompaniesandtheireffects.

Bulletin de l'association des historiens de l'art italien nn. 15-16 2009-2010

Nature Precedings, 2010

Journal of Institutional Economics, 2009

Reconstruction involves military occupation with the aim of rebuilding and reforming both formal and informal institutions along liberal democratic lines. We contend that successful reconstructions require mechanisms that make reforms credible over the long run. In the absence of a signal of sustained credible commitment, institutional reforms will not be trusted by the populace resulting in the failure of the broader reconstruction. The incentive and epistemic aspects of the credible commitment problem are analyzed. We also consider potential solutions to the problem of credible commitment. Absent such solutions, attempts to 'export' institutions via military occupation will fail or produce dysfunctional outcomes. An analysis of the numerous aspects of the credibility problem in the current reconstruction of Iraq is provided to illuminate the central arguments. *