Theoretical study of nonlinear wave equations with combined power-type nonlinearities with variable coefficients

In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is completely investigated. The threshold between the nonexistence of global in time weak solutions and non-blowing up solutions is found. For super-critical energy, two new sufficient conditions guaranteeing nonexistence of global in time solutions are given. One of them is proved for arbitrary sign of the scalar product of the initial data, while the other one is derived only for positive sign. Uniqueness and existence of local weak solutions are proved.Comment: 33 page

Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

We consider the orbital stability of solitary waves to the double dispersion equation $u_{tt} - u_{xx} + h_1 u_{xxxx} - h_2u_{ttxx} + f(u)_{xx} = 0, h_1 > 0, h_2 > 0$ with combined power-type nonlinearity $f(u) = a \left| u \right|^pu + b \left| u \right|^{2p}u, \ \ p > 0, \ \ a \in \mathbb{R}, \ \ b \in \mathbb{R},\ \ b \not = 0.$ The stability of solitary waves with velocity $c, \ c^2 < 1$ is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function $d(c)$, related to some conservation laws. We derive explicit analytical formulas for the function $d(c)$ and its second derivative for quadratic-cubic nonlinearity $f(u) = au^2 + bu^3$ and parameters $b > 0, \ c^2 \in \left[ 0, \ min \left( 1, \ \frac{h_1}{h_2} \right) \right)$. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity $f(u) = bu^3$

Behavior of the DPH fluorescence probe in membranes perturbed by drugs

1,6-Diphenyl-1,3,5-hexatriene (DPH) is one of the most commonly used fluorescent probes to study dynamical and structural properties of lipid bilayers and cellular membranes via measuring steady-state or time-resolved fluorescence anisotropy. In this study, we present a limitation in the use of DPH to predict the order of lipid acyl chains when the lipid bilayer is doped with itraconazole (ITZ), an antifungal drug. Our steady-state fluorescence anisotropy measurements showed a significant decrease in fluorescence anisotropy of DPH embedded in the ITZ-containing membrane, suggesting a substantial increase in membrane fluidity, which indirectly indicates a decrease in the order of the hydrocarbon chains. This result or its interpretation is in disagreement with the fluorescence recovery after photobleaching measurements and molecular dynamics (MD) simulation data. The results of these experiments and calculations indicate an increase in the hydrocarbon chain order. The MD simulations of the bilayer containing both ITZ and DPH provide explanations for these observations. Apparently, in the presence of the drug, the DPH molecules are pushed deeper into the hydrophobic membrane core below the lipid double bonds, and the probe predominately adopts the orientation of the ITZ molecules that is parallel to the membrane surface, instead of orienting parallel to the lipid acyl chains. For this reason, DPH anisotropy provides information related to the less ordered central region of the membrane rather than reporting the properties of the upper segments of the lipid acyl chains.Peer reviewe

Въпроси на конкурентоспособността на земеделските стопанства на България

A holistic approach for understanding, evaluating and improving the competitiveness of agricultural holdings in Bulgaria has been refined and applied. A multi-criteria assessment of the competitiveness of farms of different types is made by using survey information. A multi-criteria assessment of the level of competitiveness of agricultural holdings as a whole and with different types of product specialization was also made by using statistical data and applying the method of principal components. A comparative analysis of the level and dynamics of competitiveness of Bulgarian farms in general and with different specializations for the period 2010-2020 was also carried out. A comparative analysis of the results of the assessment of competitiveness based on survey and statistical data was made and the advantages and disadvantages of the various approaches. An assessment was made of the level and factors of competitiveness of agricultural holdings with organic production, the relationships with the main characteristics of the farmer (gender, age, etc.) were established, the most significant factors and political instruments affecting competitiveness were highlighted and the intentions were identified of organic farms in the near future. A model of CPR factor analysis and an index method for measuring competitiveness in the sheep meat sector were applied. The restructuring and diversification of agricultural cooperatives for the period after the country's integration into the EU was analyzed and a comparative assessment was made with other forms of business organizations in agriculture. The multi-criteria evaluation of alternative business models and strategies for managing the agricultural enterprise and risk was carried out, and the factors of the competitiveness of Bulgarian farms were identified. A theoretical analysis of the meso-economic level of management was made, the attitudes of alternative farmers in our country for the use of meso-institutions were established, and the relationship with agrarian competitiveness at the current stage of development of the industry was rethought. The development of agricultural holdings for the period 2007–2020 in the country was analyzed and the development of rural areas and the agrarian sector in the South Central region was compared with the general situation, by means of the Localization Index. The new trends in agricultural marketing (digitalization, intelligent marketing, etc.) are revealed, the impact on the relationship between agricultural producers and end users and the effect on the competitiveness of farms are assessed. An algorithm for the development and implementation of new models for innovative activity of small and medium-sized enterprises in agriculture is proposed, which allows effective management decisions at different levels, quantification of the index for innovative activity and easy adaptation when developing an automated system. General conclusions have been drawn up about the level, trends and factors of competitiveness of Bulgarian farms of different types and recommendations have been made for improving the scientific and evaluation methods, the system for gathering agro-information, public policies, programs and forms of intervention, and of farming strategies to improve competitiveness

A global experiment on motivating social distancing during the COVID-19 pandemic

Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e., a controlling message) compared with no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared with the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing. Controlled motivation was associated with more defiance and less long-term behavioral intention to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges

Measurement of the top quark forward-backward production asymmetry and the anomalous chromoelectric and chromomagnetic moments in pp collisions at √s = 13 TeV

Abstract The parton-level top quark (t) forward-backward asymmetry and the anomalous chromoelectric (d̂ t) and chromomagnetic (μ̂ t) moments have been measured using LHC pp collisions at a center-of-mass energy of 13 TeV, collected in the CMS detector in a data sample corresponding to an integrated luminosity of 35.9 fb−1. The linearized variable AFB(1) is used to approximate the asymmetry. Candidate t t ¯ events decaying to a muon or electron and jets in final states with low and high Lorentz boosts are selected and reconstructed using a fit of the kinematic distributions of the decay products to those expected for t t ¯ final states. The values found for the parameters are AFB(1)=0.048−0.087+0.095(stat)−0.029+0.020(syst),μ̂t=−0.024−0.009+0.013(stat)−0.011+0.016(syst), and a limit is placed on the magnitude of | d̂ t| &lt; 0.03 at 95% confidence level. [Figure not available: see fulltext.

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV

Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at root s=13 TeV

Peer reviewe

Measurement of the Jet Mass Distribution and Top Quark Mass in Hadronic Decays of Boosted Top Quarks in pp Collisions at root s=13 TeV

A measurement is reported of the jet mass distribution in hadronic decays of boosted top quarks produced in pp collisions at root s = 13 TeV. The data were collected with the CMS detector at the LHC and correspond to an integrated luminosity of 35.9 fb(-1). The measurement is performed in the lepton + jets channel of t (t) over bar events, where the lepton is an electron or muon. The products of the hadronic top quark decay t -> bW -> bq (q) over bar' are reconstructed as a single jet with transverse momentum larger than 400 GeV. The t (t) over bar cross section as a function of the jet mass is unfolded at the particle level and used to extract a value of the top quark mass of 172.6 +/- 2.5 GeV. A novel jet reconstruction technique is used for the first time at the LHC, which improves the precision by a factor of 3 relative to an earlier measurement. This highlights the potential of measurements using boosted top quarks, where the new technique will enable future precision measurements.Peer reviewe