Topological Approach to Mathematical Programs with Switching Constraints

We study mathematical programs with switching constraints (for short, MPSC) from the topological perspective. Two basic theorems from Morse theory are proved. Outside the W-stationary point set, continuous deformation of lower level sets can be performed. However, when passing a W-stationary level, the topology of the lower level set changes via the attachment of a w-dimensional cell. The dimension w equals the W-index of the nondegenerate W-stationary point. The W-index depends on both the number of negative eigenvalues of the restricted Lagrangian’s Hessian and the number of bi-active switching constraints. As a consequence, we show the mountain pass theorem for MPSC. Additionally, we address the question if the assumption on the nondegeneracy of W-stationary points is too restrictive in the context of MPSC. It turns out that all W-stationary points are generically nondegenerate. Besides, we examine the gap between nondegeneracy and strong stability of W-stationary points. A complete characterization of strong stability for W-stationary points by means of first and second order information of the MPSC defining functions under linear independence constraint qualification is provided. In particular, no bi-active Lagrange multipliers of a strongly stable W-stationary point can vanish.

Estimation of the Risk Zones Affected by Repeated Floods by Numerical Modeling

In Romania, in the last decades, was not realized any complex plan of management concerning the environmental rehabilitation of the natural riverbeds, even if there are even in present many places confronted with repeated floods. After the floods from 2004, 2005 and 2014 have been recorded in some places large deposits of sediments or contrary, in other zones with erosion and uncontrolled coastal slides. As an immediate effect, zones with risk for the local population and not only, have appeared. The present paper estimates the capacity of transport for a riverbed in natural conditions, based on the local measurements registered before and after a flood. The model is tested for a tributary of the Bistrita River, the Cracau River, near the Siret basin, an area well-known for such repeated floods sometimes even two or three recorded in the same year, as it was in 2005 and 2008. Three of these floods were confronted with human losses, many dead animals, and agricultural flooded areas. Near the analyzed watercourse there are many localities, with a high density of population. The realized numerical model for the flow with free surface was taking into account the possibility of the permanent changing of the lateral surfaces (riverbeds) during the floods. A continuous balance of the entered and transported sediments is realized, due to the erosion and sediment transportation. The time variation of the discharged liquid and the solid phases are directly connected with the sediment transport. In these conditions, the fine fractions of sediments from the bed’s structure are removed from its surface. In some places, the sediments become “armored” with the coarser part of the bed sediment. It is proposed a mathematical model to simulate the effect of both types of deposits into a fluid flow in open channels, with a movable bed. The entire alluvial stream, until the base rock, is considered with a small thickness so the non-uniformity of the grain size in the vertical distribution in riverbed could be neglected. The boundary conditions in the flood analysis consist of the upstream hydrograph and the stationary level of the downstream watercourse. Knowing the flow rate and the water levels by direct measurements, there is possible to establish the risk zones, far away from the river borders. The primary purpose of this study is to minimize the effects of such uncontrolled floods by determining the risk zones and to present a solution for increasing population safety which lives near the riverbed. Finally, some conclusions and references are mentioned.

Pharmacoepidemiological Analysis of the Use of Drugs in Elderly Patients With Hypertension at a Stationary Level

This article analyzes the frequency of prescribing drugs to elderly patients according to Beers criteria, who are in-patient treatment in the therapeutic department. 50 case histories of patients over 65 years of age over a three-month period were analyzed: from January to March 2019. The appointment sheets were analyzed using the Beers list to identify the destination of potentially not recommended drugs. According to the results of the study, it was revealed that on average 8±2 drugs were prescribed to one patient at a time, all drugs were prescribed under trade names, some of them were prescribed without indications for use. In 14 patients (28.4%), 25 non-recommended drugs were identified in different categories according to Beers criteria, where 13.6 potentially identified recommended drugs were detected in 13.6% of patients, and 5 potentially not recommended drugs were prescribed in 5.7% of patients, the use of which should be avoided in older people with certain diseases, and in 9.1% of patients 8 drugs were identified that should be used in older people with great care. All of the above allowed us to conclude that in the treatment of elderly patients, potentially not recommended medications are very often prescribed, because of which there is a risk of developing unwanted side reactions.

A New Look at Weekdays Effect of Stock Prices in the Weak Form: Evidence from Nigerian Stock Exchange

Efficiency intensity of stock exchange market has policy implications in any economy. The focus of this work is to assess the intensity of efficiency in the weak form of the Nigerian stock exchange market. This study stands to examine predictability level of Monday trading, Tuesday trading, Wednesday trading, Thursday trading and Friday trading in the Nigerian Stock Exchange (NSE). Monday NSE all share index covered August 6, 2018 to October 28, 2019; Tuesday NSE all share index covered August 7, 2018 to October 29, 2019; Wednesday NSE all share index covered August 8, 2018 to October 30, 2019; Thursday NSE all share index covered August 9, 2018 to October 31, 2019; Friday NSE all share index covered August 10, 2018 to November 1, 2019. The data was analyzed employing Jarque-Bera check for normality, ADF unit root test, graphs and GARCH term. The Jarque-Bera examination for normality indicates that all the data are normally spread. The ADF unit root shows that the factors employed were not stationary @ level series but stationary @ 1st difference. The GARCH term shows that all the variables were not significant at 5% level. From the above findings, stock prices on Mondays, Tuesdays, Wednesdays, Thursdays and Fridays stock prices studied exhibited significant random walk, the investigation therefore concludes that, NSE market is efficient in the weak form. It is thus recommended that Government should continue to allow the invisible hands to determine the direction of stock prices in order to boast NSE trading activities.

Влияние связующего и красителей на механизм туннельной люминесепнции микрокристаллов AgBr(I)

It was previously found that in emulsion microcrystals (EMC) AgBr (I) (with silver content corresponding to pBr 4), the centers responsible for tunneling recombination at T = 77 K, with a maximum of luminescence at λmax~ 560 nm when excited from light from the absorption region of AgBr (I) EMCs (λ ~ 450 nm) as a result of temperature quenching, they undergo structural transformation into centers, which, under the same excitation, provide tunneling recombination with a wavelength depending on the binder: for EMC AgBr (I) obtained in water ‒ λmax~ 720 nm, in gelatin ‒ λmax~ 750 nm. In the present work, similar structural transformations of the centers determining tunneling recombination with λmax~ 560 nm, to the centers with luminescence on λmax~ 720 nm were implemented for AgBr (I) EMCs synthesized in polyvinyl alcohol (PVA) with an increase in the content of silver ions in the emulsion (from pBr 4 to 7). Responsible for this transformation, as follows from the obtained results, are mobile interstitial silver ions Agi +, which transform these tunnel recombination centers. The effect of the binder on the recombination processes in EMC AgBr (I) is manifested in changes in the kinetics of the increase in luminescence with λmax~ 560 nm upon excitation by light from the absorption region of AgBr (I) EMC (λ ~ 450 nm) to a stationary level. For a binder whose molecules do not interact with Ag centers Agin+, n = 1, 2 (water, PVA at pBr 4), increase in luminescence with λmax~ 560 nm occurs monotonically from zero to the maximum stationary level. For a binder (in our case, G is gelatin), whose molecules with centers Agin+ (n = 1,2) form complexes (Agin0G+), the kinetics of the increase in luminescence in EMC AgBr (I) to a stationary level at λmax~ 560 nm at pBr 4 is characterized by the presence of “flash flare”. Adsorption on the surface of EMC AgBr (I) (in PVA at pBr 7) of the dye is manifested as follows: if, before the introduction of the dye, the kinetics of the increase in luminescence with λmax~ 560 nm, when excited from light from the absorption region of AgBr (I) EMC (λ ~ 450 nm) to a stationary level, “flare-up” appeared, then after the introduction of the dye, the luminescence increases with λmax~ 560 nm occurs monotonically from zero to the maximum stationary level. Studies of the “flash” of luminescence stimulated by infrared (IR) light, after the termination of the action of exciting light, showed that when the kinetics of the increase in luminescence with λmax~ 560 nm to the stationary level, it exhibits "flare-up", a "flash" stimulated by IR light is not observed at λ ~ 560 nm. In the absence of “flash flare”, a “flash” at λ ~ 560 nm is observed. From our point of view, the results obtained indicate that “flare-up burning” is due to the presence of deep centers of electron localization with a small capture cross section, and not a photochemical reaction stimulated by exciting light. Key words: AgBr (I) microcrystals, emulsions, glow centers, luminescence flare-up.

Financial Development and Economic Growth: Time Series Analysis of Economy of Pakistan

This study aims in understanding the causal relationship between financial development and economic growth. This research used annual data and applied dickey fuller test and granger causality test in order to understand stationary level and causation in variables. The results of this test give support to first hypothesis that financial development causes economic growth. While no evidence was found on the support of our second hypothesis i.e. economic growth is causing financial development.