Milnor invariants and the HOMFLYPT polynomial

We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant \bar{\mu}_J(L) vanishes for any sequence J with length at most k, then any Milnor \bar{\mu}-invariant \bar{\mu}_I(L) with length between 3 and 2k+1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the `first non vanishing' Milnor invariants can be always represented as such a linear combination.Comment: Entirely revised version (20 pages). The main result was generalized and extended to Milnor invariants of links, using new arguments. Several corollaries are given, in particular one containing the main result of the previous version. Example and References adde

Garantia da segurança nacional em condições de lei marcial e estado de emergência: Análise teórica e jurídica da experiência estrangeir

This article examines, and thoroughly analyzes, the key elements of the current state of national security processes in Ukraine. Also, ways of possible improvement of the state of ensuring the national security of Ukraine in the modern conditions of the active operation of the martial law regime are considered. It is noted that different countries of the world, at their own discretion, tend to interpret the essence and important elements of national security that exist in the world today. In addition, countries have different opportunities to take real action in relation to reforming the situation with their national security. The article focuses on the fact that truly high-quality and dynamic development of the sphere of proper provision of national security occurs in the state only when it is under threat (its state sovereignty, territorial integrity, or other important interests). The example of Israel, the United States and some other countries is not the only one where only after the emergence of this or that danger, the mechanisms and tools to overcome it begin to work in practice. Also, the importance of achieving Ukraine’s full membership in the nato military and political alliance was emphasized. After all, this military and political alliance, which unites about three dozen sovereign states, the majority of which are true liberal democracies with real rule of law and a transparent and effective state system, is recognized as the best example of such a defense alliance in history of humanity and is a good association of states close to Ukraine in spirit. It is indicated that after repelling the Russian invasion, Ukraine should focus all efforts on joining NATO.Este artículo examina y analiza a fondo los elementos clave del estado actual de los procesos de seguridad nacional en Ucrania. Además, se consideran formas de posible mejora del estado de garantizar la seguridad nacional de Ucrania en las condiciones modernas de la operación activa del régimen de ley marcial. Se advierte que diferentes países del mundo, a su criterio, tienden a interpretar la esencia y los elementos importantes de la seguridad nacional que existen en el mundo actual. Además, los países tienen diferentes oportunidades para tomar medidas reales en relación con la reforma de la situación con su seguridad nacional. El artículo se centra en el hecho de que el desarrollo verdaderamente dinámico y de alta calidad de la esfera de la provisión adecuada de seguridad nacional ocurre en el Estado solo cuando (su soberanía estatal, integridad territorial u otros intereses importantes) está bajo amenaza. El ejemplo de Israel, Estados Unidos y algunos otros países demuestra que Ucrania no es el único donde solo después de la aparición de tal o cual peligro, los mecanismos y las herramientas para superarlo comienzan a funcionar en la práctica. Además, se enfatizó la importancia de lograr la membresía plena de Ucrania en la alianza militar y política de la otan. Después de todo, esta alianza militar y política, que une a unas tres docenas de Estados soberanos, la mayoría de los cuales son verdaderas democracias liberales con un Estado de derecho real y un sistema estatal transparente y eficaz, es reconocida como el mejor ejemplo de tal alianza de defensa en la historia de la humanidad y es una buena asociación de Estados cercanos a Ucrania en espíritu. Se indica que, tras repeler la invasión rusa, Ucrania debería centrar todos sus esfuerzos en unirse a la OTAN.Este artigo examina e analisa minuciosamente os principais elementos do estado atual dos processos de segurança nacional na Ucrânia. Além disso, são consideradas formas de possível melhoria do estado de garantia da segurança nacional da Ucrânia nas condições modernas da operação ativa do regime de lei marcial. Observa-se que diferentes países do mundo, a seu próprio critério, tendem a interpretar a essência e os elementos importantes da segurança nacional que existem no mundo atual. Além disso, os países têm diferentes oportunidades de tomar medidas reais em relação à reforma da situação de sua segurança nacional. O artigo enfoca o fato de que o desenvolvimento verdadeiramente dinâmico e de alta qualidade da esfera de fornecimento adequado de segurança nacional ocorre no Estado somente quando ele está sob ameaça (sua soberania estatal, integridade territorial ou outros interesses importantes). O exemplo de Israel, dos Estados Unidos e de alguns outros países não é o único em que, somente após o surgimento desse ou daquele perigo, os mecanismos e as ferramentas para superá-lo começam a funcionar na prática. Além disso, foi enfatizada a importância de a Ucrânia se tornar membro pleno da aliança militar e política da otan. Afinal, essa aliança militar e política, que une cerca de três dúzias de Estados soberanos, a maioria dos quais são verdadeiras democracias liberais com um verdadeiro estado de direito e um sistema estatal transparente e eficaz, é reconhecida como o melhor exemplo dessa aliança de defesa na história da humanidade e é uma boa associação de Estados próximos à Ucrânia em espírito. É indicado que, após repelir a invasão russa, a Ucrânia deve concentrar todos os esforços para ingressar na OTAN

Проблеми правового регулювання процедури розірвання шлюбу в порядку окремого провадження

The article is devoted to the study of the peculiarities of applying the norms of national civil procedural and family law when courts of civil jurisdiction consider the application on divorce from the spouses in special proceedings. Attention is drawn to the problems in determining the content of the application, the subject composition, jurisdiction and the particularities of considering this category of cases. The analysis of one of the court rulings allowed the author to draw attention to inconsistencies in the civil procedural law.The work stresses on the consolidation of the possibility of considering such a case in the special proceedings by the court, but the absence of norms on the peculiarities of considering this category of cases gives rise to an ambiguity in the interpretation of certain norms of the civil procedural legislation. The analysis of literary sources also indicates a lack of studies of these issues.When considering the peculiarities of the subject composition, the author draws attention to the absence in the content of the civil procedural legislation of such an entity as the “spouses” with a legislatively fixed provision in the Civil Procedural Code of Ukraine of the need to participate in special proceedings of an applicant as a person applying to the court and, on the other hand, interested parties. The impossibility of applying the rules of jurisdiction in this case is proved by analogy with the rules of jurisdiction in cases of legal action. When considering the issues related to the peculiarities of the consideration of these categories of cases by courts, attention is drawn to the uncertainty of the civil procedural legislation on the timing of a decision by a court in such cases, on the procedural and legal consequences of withdrawal of a divorce application by spouses and on the procedural fixation of the consequences of this event by the court.Taking an account of the given factors, it is concluded that it is more expedient and transparent to consider the issue of divorce process according to the rules of ordinary legal proceedings, and not a special one.Статья посвящена исследованию особенностей применения норм национального гражданского процессуального и семейного права при рассмотрении судами гражданской юрисдикции в порядке особого производства заявления супругов о расторжении брака. Обращается внимание на проблемы в определении содержания заявления, субъектного состава, подсудности и особенностей рассмотрения этой категории дел. Анализ одного из определений суда позволил автору обратить внимание на несогласованности в гражданском процессуальном законодательстве.Статтю присвячено дослідженню особливостей застосування норм національного цивільного процесуального та сімейного права при розгляді судами цивільної юрисдикції в порядку окремого провадження заяви подружжя про розірвання шлюбу. Розглянуто проблеми у визначенні змісту заяви, суб’єктного складу, підсудності та особливостей розгляду цієї категорії справ. Аналіз однієї з судових ухвал засвідчив наявність  суперечностей у цивільному процесуальному законодавстві

Experimental Study of Residual Stresses in Metal Parts Obtained by Selective Laser Melting

AbstractHigh local temperature gradients occur at additive manufacturing by selective laser melting of powder. This gives rise to undesirable residual stresses, deformations, and cracks. To understand how to control the formation of the residual stresses, a reliable method is necessary for measuring their distribution in the fabricated part. It is proposed to cut the part into thin plates and to reconstruct the residual stresses from the measured deformation of the plates. This method is tested on beams with square cross-section built from stainless steel. The beams were cut by electrical discharge machining and chemically etched. The obtained stress profile in vertical transversal direction slightly increases from the top to the bottom of the beam. This dependency is confirmed by numerical modeling. The measured stress profile agrees with the known results by other authors

Time-resolved Visualization of Laser Beam Melting of Silica Glass Powder

AbstractSilica glass is an inorganic dielectric material that can be used for laser beam melting without cracking. However, the extremely high viscosity makes consolidation of powder very slow. To study the dynamics of consolidation, a 10.6μm laser beam was directed on the powder layer deposited on the solid substrate of the same material. The laser-interaction zone was lighted with green laser and filmed with a high-speed camera at 6000 fps. The process develops steadily. Neither fluctuation nor droplets are observed. An expanding consolidation zone is observed. Viscous merging of softened powder particles is supposed to be the principal mechanism of consolidation. Mathematical model based on this mechanism confirms formation of the consolidated zone in the center. Both the experiment and the model indicate that consolidation looks like propagation of a sharp front. Comparison of the experiments and the calculations estimates the consolidation front temperature of about 1800-1900K

Minimum length of suspended sediment yield time-series for a proper estimation of spatio-temporal variability of erosion rates in river basins

River suspended sediment yield (R) is one of the proxies of erosion activity and mechanical denudation in river basins, that can vary greatly both in space and time. A number of R-databases have been collected and permitted to reveal regional and global patterns of erosion. One of the main shortcomings of these databases is the high presence of relatively short lime-scries, which influences greatly the reliability of resultant assessments of spatial erosion patterns. It is necessary to determine the minimum time-series length reliable for assessment of suspended sediment yield spatio-temporal variability, erosion rate mapping and theoretical issues. The author's original method was used to analyze long term time-series from 84 hydrological stations over the former USSR and determine the I values of 9.1 ± 1.2 and 7.611.2 years for assessment of spatial and temporal variability oftf, rcspcciivcly. In case of spatial variability of R in small river basins, reliable time series are 10+ years in lowland landscapes and 6-7 years in highlands, for medium and large basins the /-values are 5 and 10 years respectively. Given that the majority of hydrological stations are located in lowlands and low mountains, the author recommends to base regional and global hydrogeomorphological studies on suspended sediment yield time series not shorter than 10-11 years

Aeolian-Accumulative complex sarykum as a unique geomorphic object Of Russia: Structure, genesis and sands sources

Acolian-accumulativc complcx Sarykum is one of the highest isolated (i.e. formed away from the deserts) sandy land forms in Eurasia, located within the Tcrck-Sulak lowland plain at the north-eastern foothill of the Caucasus Mountains, 16-17 km towards WNW of the Makhachkala City port of Caspian Sea (Republic of Dagestan, Russia). On the basis of particle size distribution and mineralogical analysis of 59 sandy samples, the heterogeneous structure of the complcx is defined. The coarscst sandy material (modal values arc 352 micron and more) composes the central dunc-ridgc segment of Sarykum (of so-called Great (or West) Sarykum). The further from the dune constructions to the periphery, the thinner the average dimension of the sand particles and smaller the modal values (249 micron and less) of their granulomere spectra. This grain size distribution can be explained not only by windy sorting of the sands and further acolian recast of dunc-ridgc segment, but also by spatial features of the facial changes during the period of initial sandy accumulation, and also by the differences in composition of rocks, which were the sources of denudation. In the vertical structure of Sary kum the heterogeneity is also expressed. It is associated with temporary changcs of sandy sedimentation conditions in the region. So, the dunc-ridgc segment of Great Sarykum can be represented as a system of consistently accumulated sandy layers (lenses?) (which includes the gravelly sands), which differ in composition and age, having apparently the coarscst content in the middle part of its vertical geological cross-section. The material of overwhelming majority of the selected samples belongs to mineral group of quartz sands (quartz contcnt is over 90%) and subgroup of quartz subarkosc (quartz contcnt is 80-90%). Moreover, the acolian (deflated) sands of the dunc-ridgc segment and its underlying cross-bcddcd sands of Great Sarykum entirely belong to the first group; the hilly and peripheral sands, which characterized by fine granulomctry, refer to the second mineral subgroup. The Sarykum's structure is due to the combination of gravelly sands, formed by the river Shura-Ozcn' dcltaic accumulation in the Late Quaternary, and sandy (with gravels and pcbbccs) deposits proluvially and dcluvially dislocated to the recent Sarykum massif territory from the slopes of the nearby Narat-Tubc mountain range. The mixing of originally and compositionally different sediments that formed the Sarykum complcx, likely have the complicated history, following by the staged changcs of the periglacial landscape-climatic conditions in the Late Quaternary