Ljubisa Nesic

p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

Adelic Path Integrals for Quadratic Lagrangians

Feynmans path integral in adelic quantum mechanics is considered. The propagator for one-dimensional adelic systems with quadratic Lagrangians is analytically evaluated. Obtained exact general formula has the form which is invariant under interchange of the number fields ℝ and ℚp.

Dimensional analysis in physics and the Buckingham theorem

Dimensional analysis is a simple, clear and intuitive method for determining the functional dependence of physical quantities that are of importance to a certain process. However, in physics textbooks, very little space is usually given to this approach and it is often presented only as a diagnostic tool used to determine the validity of dependences otherwise obtained. This paper presents the basics of dimensional analysis in two cases: the resistance force of the fluid that occurs when a body moves through it and the speed of propagation of waves on water. After that, a general approach to dimensional analysis based on the Buckingham theorem is shown. The material presented in the paper could be useful to both students of physics and physics graduates.

Signature change in p-adic and noncommutative FRW cosmology

The significant matter for the construction of the so-called no-boundary proposal is the assumption of signature transition, which has been a way to deal with the problem of initial conditions of the universe. On the other hand, results of Loop Quantum Gravity indicate that the signature change is related to the discrete nature of space at the Planck scale. Motivated by possibility of non-Archimedean and/or noncommutative structure of space–time at the Planck scale, in this work we consider the classical, p-adic and (spatial) noncommutative form of a cosmological model with Friedmann–Robertson–Walker (FRW) metric coupled with a self-interacting scalar field.

Towards Adelic Noncommutative Quantum Mechanics

A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools embedded in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted. A few relations between noncommutativity and nonarchimedean spaces as well as similarities between corresponding quantum theories on them are pointed out. An extended Moyal product in a proposed form of adelic noncommutative quantum mechanics is considered. We suggest some question for future investigations.

Two-oscillator Kantowski–Sachs model of the Schwarzschild black hole interior

In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum, homogeneous and anisotropic Kantowski–Sachs minisuperspace cosmological model, is considered. Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model is presented in a classical, a p-adic and a noncommutative case. Then, within the standard quantum approach Wheeler–DeWitt equation and its general solutions, i.e. a wave function of the model is written, and then an adelic wave function is constructed. Finally, thermodynamics of the model is studied by using the Feynman–Hibbs procedure.

p-Adic quantum cosmology

Abstract p -Adic quantum cosmology is one of the considerable applications of p -adic quantum theory, which takes into account possible nonarchimedean (ultrametric) aspects of space-time. For this reason, we consider minisuperspace cosmological models in the framework of p -adic and adelic quantum mechanics. In particular, we investigate the de Sitter model and obtain p -adic and adelic wave functions, which are briefly discussed.

Preface to the Proceedings of p-Adics.2015 Conference

This special issue of FU Phys Chem Tech is dedicated to Professor Radosav M. Palic on the occasion of his 70 th birthday. Dr. Palic has made important contributions in many areas of chemistry, his main interest being the chemistry of volatile plant metabolites and their antimicrobial activity. He was the pioneer of the phytochemical research at the University of Nis. The authors of the papers published in this issue (all manuscripts underwent a rigorous peer-review process) are his former students and/or his scientific collaborators, who are grateful to him for his contribution to the development of chemistry not only at the University of Nis but also in Serbia. PREDGOVOR SPECIJALNOM BROJU CASOPISA FU Phys Chem Tech, POSVECENOM PROFESORU RADOSAVU M. PALICU, U CAST NJEGOVOG 70. ROĐENDANA Ovaj specijalni broj casopisa FU Phys Chem Tech je posvecen profesoru Radosavu M. Palicu, u cast njegovog 70. rođendana. Dr Palic je dao znacajan doprinos razlicitim oblastima hemije, a najvise se bavio proucavanjem hemije isparljivih biljnih metabolita i njihovom antimikrobnom aktivnoscu. Profesor Palic je bio pionir fitohemijskih istraživanja na Univerzitetu u Nisu. Autori radova objavljenih u ovom broju (svi rukopisi su podvrgnuti naucnoj recenziji) su njegovi bivsi studenti i/ili saradnici, koji su mu zahvalni na svemu sto je on ucinio za razvoj hemije ne samo na Univerzitetu u Nisu, vec i u Srbiji uopste.Breastfeeding is considered as the best feeding choice for newborns. As some infants could not be fed by their mothers, infant formulas remain an alternative to breast-milk and thus, play an important role in infant’s diet. During the years, infant formula manufacturers have made changes to formulas in order to closely match human milk composition. However, the control of the infant formula quality is mandatory in order to ensure that infants everywhere are well nourished. Riboflavin, or vitamin B 2 , is essential for normal infant growth, so infant formulas had to contain the required levels of this vitamin. Therefore, in this work, it was developed and validated a simple and accurate HPLC-FLD method for assessment of vitamin B 2 content in infant formulas (linearity range=0.02−2.0 µg/mL; LOQ=0.033 µg/mL; accuracy>96%, respectively). The main advantages of herein described protocol are the use of small volumes of toxic solvents and reagents, simple sample pre-treatment (without enzymatic digestion) and short time of analysis. Ten best-selling infant formulas on Serbian market were assayed for riboflavin content employing the described method. Significant differences were found in the vitamin B 2 levels (from 68.60 to 131.18 µg per 100 mL of prepared milk) in formulas produced by different manufacturers. The values obtained for riboflavin content in all samples mainly correspond to the declared amounts by manufacturer. The conducted quality monitoring revealed that infant formulas from Serbia comply with the nutritional needs of infants with regard to vitamin B 2 .

KANTOWSKI-SACHS MINISUPERSPACE COSMOLOGICAL MODEL ON NONCOMMUTATIVE SPACE

This special issue of FU Phys Chem Tech is dedicated to Professor Radosav M. Palic on the occasion of his 70 th birthday. Dr. Palic has made important contributions in many areas of chemistry, his main interest being the chemistry of volatile plant metabolites and their antimicrobial activity. He was the pioneer of the phytochemical research at the University of Nis. The authors of the papers published in this issue (all manuscripts underwent a rigorous peer-review process) are his former students and/or his scientific collaborators, who are grateful to him for his contribution to the development of chemistry not only at the University of Nis but also in Serbia. PREDGOVOR SPECIJALNOM BROJU CASOPISA FU Phys Chem Tech, POSVECENOM PROFESORU RADOSAVU M. PALICU, U CAST NJEGOVOG 70. ROĐENDANA Ovaj specijalni broj casopisa FU Phys Chem Tech je posvecen profesoru Radosavu M. Palicu, u cast njegovog 70. rođendana. Dr Palic je dao znacajan doprinos razlicitim oblastima hemije, a najvise se bavio proucavanjem hemije isparljivih biljnih metabolita i njihovom antimikrobnom aktivnoscu. Profesor Palic je bio pionir fitohemijskih istraživanja na Univerzitetu u Nisu. Autori radova objavljenih u ovom broju (svi rukopisi su podvrgnuti naucnoj recenziji) su njegovi bivsi studenti i/ili saradnici, koji su mu zahvalni na svemu sto je on ucinio za razvoj hemije ne samo na Univerzitetu u Nisu, vec i u Srbiji uopste.Breastfeeding is considered as the best feeding choice for newborns. As some infants could not be fed by their mothers, infant formulas remain an alternative to breast-milk and thus, play an important role in infant’s diet. During the years, infant formula manufacturers have made changes to formulas in order to closely match human milk composition. However, the control of the infant formula quality is mandatory in order to ensure that infants everywhere are well nourished. Riboflavin, or vitamin B 2 , is essential for normal infant growth, so infant formulas had to contain the required levels of this vitamin. Therefore, in this work, it was developed and validated a simple and accurate HPLC-FLD method for assessment of vitamin B 2 content in infant formulas (linearity range=0.02−2.0 µg/mL; LOQ=0.033 µg/mL; accuracy>96%, respectively). The main advantages of herein described protocol are the use of small volumes of toxic solvents and reagents, simple sample pre-treatment (without enzymatic digestion) and short time of analysis. Ten best-selling infant formulas on Serbian market were assayed for riboflavin content employing the described method. Significant differences were found in the vitamin B 2 levels (from 68.60 to 131.18 µg per 100 mL of prepared milk) in formulas produced by different manufacturers. The values obtained for riboflavin content in all samples mainly correspond to the declared amounts by manufacturer. The conducted quality monitoring revealed that infant formulas from Serbia comply with the nutritional needs of infants with regard to vitamin B 2 .

Brownian Motion, Fractal Structure and Verification of A. Einstein’s Formula

The work offers a simple experimental verification of A. Einstein and M. Smoluhovski’s formula for Brownian motion. In this experiment we used latex solved in water, glycerin and alcohol while the observations and recording were done with a binocular optical microscope and a digital camera. Video material is recorded in separate files put on the Internet and can be downloaded and used for demonstration in class or further computer processing.