Discreteness of the Spectrum of Second-Order Differential Operators and Associated Embedding Theorems

AbstractNecessary and sufficient conditions and also simple sufficient conditions are given for the self-adjoint operators associated with the second-order linear differential expressionτ(y)=1w(−(py′)′+qy) on [a,b) to have discrete spectrum. Here the coefficients of τ are non-negative and satisfy minimal smoothness conditions. These results follow from compact embedding theorems from a weighted one-dimensional Sobolev space with norm∫ab(p∣f′∣r+q∣f∣r))1/r into a weighted Banach space with norm(∫abw∣f∣s)1/s

POSSIBILITIES, LIMITATIONS AND ECONOMIC ASPECTS OF ARTIFICIAL INTELLIGENCE APPLICATIONS IN HEALTCARE

The increasing importance of achieving sustainable development is largely positively influenced the emergence and increasing the level of application of artificial intelligence in different spheres of human activity, but especially in the field of health care. It is this trend and initiated that in work devote special attention to precisely to the analysis of potential opportunities, and economic effects of the use of artificial intelligence in the direction of improving efficiency, but the economic effects of health car

SMART CITY: A CONTEMPORARY CONCEPT OF URBAN SUSTAINABLE DEVELOPMENT

Migration from rural areas to cities, beside to migration of highly educated labor, are becoming one of the most significant challenges in the contemporary urban environment. Increasingly and extensively influx of population from rural areas into cities, with climate and lifestyle changes, additionally exposed city government to challenges for optimal city functioning and sustainable urban development. These challenges as initiatives to improve the quality of life, higher efficiency and preservation of the environment, with the accelerated development of new technologies, are resulted in the emergence of the Smart City concept. The Smart City concept represents the dominant direction of urban development based on the digital transformation of the city and principles of sustainable development. At its core, the concept involves the digital transformation of the city towards achieving greater efficiency of the city administration, higher quality of life, reducing the exploitation of resources, but also reducing the negative impact on the environment. The importance of digital transformation of cities and the importance of sustainable development are initiated the authors, to present in this paper the basic determinants of the Smart City concept as integral part of the urban sustainable development strateg

Slovenian Grassland Society: Science, Profession and Practice

The Slovenian Grassland Society (SGS) was established in 1993. It has around 120 members. A half of members are active farmers, around 10% are scientists, the rest are employed in extension services or other agricultural enterprises (seed companies, administration bodies, etc.

TRADE SECRETS - SECURITY AND LEGAL ASPECT

The struggle for the dominance of competition is increasingly being transferred from physical to virtual arena, and therefore the application of new technologies is becoming an increasingly important basis for faster development, but it is becoming increasingly important weapon in the struggle for the dominance of competition in the new (digital) economy. The aforementioned trends in the foreground are even more emphasized than they were in the past years, the need to improve the protection of intellectual property, and the enhancement of the protection of trade secrets from increasingly intense industrial espionage and increasingly frequent cyber attacksIt is this trend that has been mentioned and initiated to pay special attention to the analysis of the possibilities and potential possibilities for improvement of the security and legal system of protection of sent secrets as an integral part of the intellectual propert

BASIC PRINCIPLES OF CIRCULAR ECONOMY WITH SPECIAL FOCUS ON SUSTAINABLE CONSUMPTION "Y" AND "Z" GENERATION

The growth of world population, market globalization, unethical business practices of large companies, irresponsible consumer behavior threatening to completely degrade the health of the planet. Consumerist society requires the purchase and possession of things as imperatives to a good life, which in turn leads to the creation of large quantities of waste. The concept of sustainable development and the circular economy have long been present in academic literature, but the question is how much they are represented in practice. Planet needs "green" consumers whose consumption will not affect the health of the environment. From the young generations, Y and Z, much is expected. Are they ready to initiate change and make the planet a healthier place to live for both existing and future generations? There are a number of studies on this topic and opinions are of course divided. One group of authors consider them agents of change, while others point out that their behavior is not very different from their predecessors and that it is necessary to provide them with education on all current environmental issues and problems

W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions

In an attempt to improve on our earlier W3 theory [J. Chem. Phys. {\bf 120}, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations ($\hat{T}_4$), inclusion of connected quintuple excitations ($\hat{T}_5$), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the ATcT (Active Thermochemical Tables) Thermochemical Network. We found that the CCSDTQ$-$CCSDT(Q) difference converges quite rapidly with the basis set, and that the formula 1.10[CCSDT(Q)/cc-pVTZ+CCSDTQ/cc-pVDZ$-$CCSDT(Q)/cc-pVDZ] offers a very reliable as well as fairly cost-effective estimate of the basis set limit $\hat{T}_4$ contribution. The largest $\hat{T}_5$ contribution found in the present work is on the order of 0.5 kcal/mol (for ozone). DBOC corrections are significant at the 0.1 kcal/mol level in hydride systems. . Based on the accumulated experience, a new computational thermochemistry protocol for first-and second-row main-group systems, to be known as W4 theory, is proposed. Our W4 atomization energies for a number of key species are in excellent agreement (better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1 kJ/mol) with the latest experimental data obtained from Active Thermochemical Tables. A simple {\em a priori} estimate for the importance of post-CCSD(T) correlation contributions (and hence a pessimistic estimate for the error in a W2-type calculation) is proposed.Comment: J. Chem. Phys., in press; electronic supporting information available at http://theochem.weizmann.ac.il/web/papers/w4.htm

Paleolinguistics brings more light on the earliest history of the traditional Eurasian pulse crops

Traditional pulse crops such as pea, lentil, field bean, bitter vetch, chickpea and common vetch originate from Middle East, Mediterranean and Central Asia^1^. They were a part of human diets in hunter-gatherers communities^2^ and are one of the most ancient cultivated crops^3,4^. Europe has always been rich in languages^5^, with individual families still preserving common vocabularies related to agriculture^6,7^. The evidence on the early pulse history witnessed by the attested roots in diverse Eurasian proto-languages remains insufficiently clarified and its potential for supporting archaeobotanical findings is still non-assessed. Here we show that the paleolinguistic research may contribute to archaeobotany in understanding the role traditional Eurasian pulse crops had in the everyday life of ancient Europeans. It was found that the Proto-Indo-European language^8,9^ had the largest number of roots directly related to pulses, such as *arnk(')- (a leguminous plant), *bhabh- (field bean), *erəgw[h]- (a kernel of leguminous plant; pea), *ghArs- (a leguminous plant), *kek-, *k'ik'- (pea) and *lent- (lentil)^10,11,12^, numerous words subsequently related to pulses^13,14^ and borrowings from one branch to another^15^, confirming their essential place in the nutrition of Proto-Indo-Europeans^16,17,18^. It was also determined that pea was the most important among Proto-Uralic people^19,20,21^, while pea and lentil were the most significant in the agriculture of Proto-Altaic people^22,23,24^. Pea and bean were most common among Caucasians^25,26^, Basques^27,28^ and their hypothetical common forefathers^29^ and bean and lentil among the Afro-Asiatic ancestors of modern Maltese^30^. Our results demonstrate that pulses were common among the ancestors of present European nations and that paleolinguistics and its lexicological and etymological analysis may be useful in better understanding the earliest days of traditional Eurasian crops. We believe our results could be a basis for advanced multidisciplinary approach to the pulse crop domestication, involving plant scientists, archaeobotanists and linguists, and for reconstructing even earlier periods of pulse history

The Crystal Structure and Conformation of bis(N-methyl-5-chlorosalicylideneiminato)nickel(II) and bis(N-ethyl-5-chlorosalicy lideneiminato)nickel(II)

The crystal structures of bis(N-methyl-5-chlorosalicylideneiminato) nickel(II) (A) and bis(N-ethyl-5-chlorosalicylideneiminato) nickel(II) (B) have been determined by X-ray structure analysis using heavy atom method and refined by fuU matrix leastsquares procedure to R values of 0.044 and 0.040 for (A) and (B), respectively. Both structures have molecular centre of symmetry and the nickel atom in a planar coordination. Molecules of both complex compounds have »stepped« conformation with distinct difference in the step heights: 0.121 and 0.702 A in (A) and (B), respectively. The Ni-O and Ni-N bond lengths are 1.818 and 1.924 A in (A), and \u271.830 and 1.916 A in (B)

Esubacute acidosis in rumen of high-yield dairy cows: Prevalence and prevention

The objective of the investigations presented in this paper was to establish the frequency of the incidence of subacute acidosis in the rumen of cows (SARA) in the first three months of lactation and the possibilities for its prevention using a mineral mix based on bentonite, zeolite, magnesium oxide, and sodium bicarbonate (Mix plus). The values obtained for the rumen pH content show that subacute rumen acidosis occurs in in 20 percent of the examined cows in the early stage of lactation. For these investigations, cows in early stages of lactation were chosen and divided into 2 groups. Cows of the experimental group were administered a fodder mix which contained the mineral mix for a buffer effect (Mix plus). The average values of the rumen pH content in the control and the experimental group of cows at the beginning and on the 30th day of the experiment were approximately the same and did not differ significantly (p>0.05). On the 60th day of the experiment, the values for the electrochemical reaction of the rumen content for the control group amounted to an average of 6.219±0.18, and for the experimental group of cows it was 6.772±0.23. The obtained difference was statistically very significant (p<0.001). At the end of the experiment, on the 90th day, the average pH value of the rumen content of cows of the control group was 6.308±0.16, while this value in the experimental group of cows was significantly higher and amounted to 6.676±0.29 (p<0.01)