Low energy universality and scaling of Van der Waals forces

At long distances interactions between neutral ground state atoms can be described by the Van der Waals potential V(r) =-C6/r^6-C8/r^8 - ... . In the ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts given by an effective range expansion p cot d0 (p) = -1/a0 + r0 p^2/2 + ... in terms of the scattering length a0 and the effective range r0. We show that while for these potentials the scattering length cannot be predicted, the effective range is given by the universal low energy theorem r0 = A + B/a0+ C/a0^2 where A,B and C depend on the dispersion coefficients Cn and the reduced di-atom mass. We confront this formula to about a hundred determinations of r0 and a0 and show why the result is dominated by the leading dispersion coefficient C6. Universality and scaling extends much beyond naive dimensional analysis estimates.Comment: 4 pages, 3 figure

Features Implementation of Environmental Innovation in Ukraine

Given the pace of global economic growth, industrial development, mining and processing industries, whose products are targeted including in meeting their social needs, objectively there is a risk reduction of available natural resources to a critical point, and the deterioration of the environment and endangering the people because of technological issues and environmental issues. Based on these risks at present and in the future effectiveness of social production will fully depend on the efficiency of environmental protection, which should pay attention not only state and public nature protection organizations, and especially enterprise industries, which rely implementation and responsibilities adherence to environmental regulations and technological standards of production and economic activity

Features Implementation of Environmental Innovation in Ukraine

Given the pace of global economic growth, industrial development, mining and processing industries, whose products are targeted including in meeting their social needs, objectively there is a risk reduction of available natural resources to a critical point, and the deterioration of the environment and endangering the people because of technological issues and environmental issues. Based on these risks at present and in the future effectiveness of social production will fully depend on the efficiency of environmental protection, which should pay attention not only state and public nature protection organizations, and especially enterprise industries, which rely implementation and responsibilities adherence to environmental regulations and technological standards of production and economic activity

Value of dangers, threats and risks in formation of costs to suport economic security

У статті надане змістовне розмежування понять «ризик», «небезпека», «загроза» та їхнє значення у питаннях забезпечення економічної безпеки підприємства; вивчена сутність категорії «загроза» як чинника з негативним впливом на рівень (стан або міру) економічної безпеки підприємства; встановлено зв’язок між загрозами, заходами протидії загрозам і витратами на забезпечення економічної безпеки підприємства.В статье представлено смысловое разграничение понятий «риск», «опасность», «угроза» и их значение в вопросах обеспечения экономической безопасности пред- приятия; изучена сущность категории «угроза» как фактора с отрицательным влиянием на уровень (состояние или меру) экономической безопасности предприятия; установлена связь между угрозами, мероприятиями по противодействию угрозам и расходами на обеспечение экономической безопасности предприятия.The article provided a meaningful distinction between "risk", "threat" and their importance in ensuring economic security; understood the essence of the category "threat" as a factor in the negative impact on the level (state or extent) economic security; The relationship between threats, measures to counter threats and costs of providing economic security

Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy

Time-fractional partial differential equations are nonlocal in time and show an innate memory effect. In this work, we propose an augmented energy functional which includes the history of the solution. Further, we prove the equivalence of a time-fractional gradient flow problem to an integer-order one based on our new energy. This equivalence guarantees the dissipating character of the augmented energy. The state function of the integer-order gradient flow acts on an extended domain similar to the Caffarelli-Silvestre extension for the fractional Laplacian. Additionally, we apply a numerical scheme for solving time-fractional gradient flows, which is based on kernel compressing methods. We illustrate the behavior of the original and augmented energy in the case of the Ginzburg-Landau energy functional

Efimov states in asymmetric systems

The conditions for occurrence of the Efimov effect is briefly described using hyperspherical coordinates. The strength of the effective hyperradial $\rho^{-2}$ potential appearing for two or three large scattering lengths is computed and discussed as function of two independent mass ratios of the three constituent particles. The effect is by far most pronounced for asymmetric systems with three very different masses. One Efimov state may by chance appear in nuclei. Many states could be present for systems with one electron and two neutral atoms or molecules. Estimates of the number of states and their sizes and energies are given.Comment: 7 pages, 3 figure