Dipole-Mode Vector Solitons

We find a new type of optical vector soliton that originates from trapping of a dipole mode by a soliton-induced waveguide. These solitons, which appear as a consequence of the vector nature of the two component system, are more stable than the previously found optical vortex-mode solitons and represent a new type of extremely robust nonlinear vector structure.Comment: Four pages with five eps figure

Observation of dipole-mode vector solitons

We report on the first experimental observation of a novel type of optical vector soliton, a {\em dipole-mode soliton}, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium employing two different processes: a phase imprinting, and a symmetry-breaking instability of a vortex-mode vector soliton. The experimental results display remarkable agreement with the theory, and confirm the robust nature of these radially asymmetric two-component solitary waves.Comment: 4 pages, 8 figures; pictures in the PRL version are better qualit

Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates

We investigate dark-bright vector solitary wave solutions to the coupled non-linear Schr\"odinger equations which describe an inhomogeneous two-species Bose-Einstein condensate. While these structures are well known in non-linear fiber optics, we show that spatial inhomogeneity strongly affects their motion, stability, and interaction, and that current technology suffices for their creation and control in ultracold trapped gases. The effects of controllably different interparticle scattering lengths, and stability against three-dimensional deformations, are also examined.Comment: 5 pages, 5 figure

CALCULATION OF THE DIGITAL TWIN OF THE SALES FUNNEL

Commercial activity has always been influenced by the competitive environment and its spread to the online space is the next stage of development and a defining trend for the nearest time horizon. The changes in the business landscape influenced by COVID19 pose new challenges for marketers and entrepreneurs. It is necessary to use the forced sharp increase in online interaction with consumers. The course towards the digital economy determines the use of scientific, mathematical methods to optimize the target indicators of economic activity. These global shifts in business interactions are generating innovative tools for measuring business results and transforming old practices to meet new market realities. This is the basic condition for the sustainability of doing business in any industry. This study is devoted to the development of a theoretical description of the process of multi-stage interaction with a consumer pool. To solve this problem, a mathematical model has been developed, the basis of which is digital information interaction, starting from the stage of determining the target audience and ending with the complete completion of a commercial transaction. This article presents the results of modeling sales funnel, as the basis for the software of a modern market analyst, using a cross-system approach. In contrast to the classical sales funnel, the presented algorithms allow using the multidimensional conversion funnel not only for assessing business results for the reporting period. Thanks to the flow of model arguments in real time, it becomes possible to optimize the business process by moving to the concept of leading economic indicators.In practice, this means the ability to implement effective business planning on digital platforms. The arguments of the mathematical model are Internet statistics, the dynamics of consumer preferences, the history of the business process accumulated in the big data system. At the same time, the means of queuing theory, differential calculus, economic and mathematical modeling are involved, based on indicators such as KPI (Key Performance Indicators), CTR (click-through rate), CR (Conversion rate). This made it possible to formulate the concept of a digital twin of a commercial process and its transformation, convenient for practical applications, into a conversion funnel for embedding into algorithms implemented on a computer

Observation of discrete vortex solitons in optically-induced photonic lattices

We report on the frst experimental observation of discrete vortex solitons in two-dimensional optically-induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.Comment: 4pages, 5 colour figures. to appear in PR

РАСЧЕТ ЦИФРОВОГО ДВОЙНИКА ВОРОНКИ ПРОДАЖ

Commercial activity has always been influenced by the competitive environment and its spread to the online space is the next stage of development and a defining trend for the nearest time horizon. The changes in the business landscape influenced by COVID19 pose new challenges for marketers and entrepreneurs. It is necessary to use the forced sharp increase in online interaction with consumers. The course towards the digital economy determines the use of scientific, mathematical methods to optimize the target indicators of economic activity. These global shifts in business interactions are generating innovative tools for measuring business results and transforming old practices to meet new market realities. This is the basic condition for the sustainability of doing business in any industry. This study is devoted to the development of a theoretical description of the process of multi-stage interaction with a consumer pool. To solve this problem, a mathematical model has been developed, the basis of which is digital information interaction, starting from the stage of determining the target audience and ending with the complete completion of a commercial transaction. This article presents the results of modeling sales funnel, as the basis for the software of a modern market analyst, using a cross-system approach. In contrast to the classical sales funnel, the presented algorithms allow using the multidimensional conversion funnel not only for assessing business results for the reporting period. Thanks to the flow of model arguments in real time, it becomes possible to optimize the business process by moving to the concept of leading economic indicators.In practice, this means the ability to implement effective business planning on digital platforms. The arguments of the mathematical model are Internet statistics, the dynamics of consumer preferences, the history of the business process accumulated in the big data system. At the same time, the means of queuing theory, differential calculus, economic and mathematical modeling are involved, based on indicators such as KPI (Key Performance Indicators), CTR (click-through rate), CR (Conversion rate). This made it possible to formulate the concept of a digital twin of a commercial process and its transformation, convenient for practical applications, into a conversion funnel for embedding into algorithms implemented on a computer.Коммерческая деятельность всегда испытывала воздействие конкурентной среды, и онлайн-торговля является следующей ступенью развития и определяющим трендом на ближайшее время. Произошедшие под влиянием COVID-19 изменения в бизнес-ландшафте ставят перед маркетологами и предпринимателями новые задачи. Необходимо использовать вынужденный резкий рост онлайн-взаимодействия с потребителями. Курс на цифровую экономику обуславливает применение научных, математических методов для оптимизации целевых показателей экономической деятельности. Такие глобальные перемены в бизнес-взаимодействии порождают инновационные инструменты для оценки результатов коммерции и трансформируют прежние методики для соответствия новым реалиям рынка. Это является базовым условием устойчивости ведения бизнеса в любой отрасли. Настоящее исследование посвящено разработке теоретического описания процесса многоступенчатого взаимодействия с потребительским пулом. Для решения задачи формализации данного процесса разработана математическая модель, основу которой составляет информационное цифровое взаимодействие от этапа определения целевой аудитории до полного завершения коммерческой сделки.В предлагаемой статье изложены результаты работы по моделированию sales funnel как основы программного обеспечения современного аналитика рынка с применением кросс-системного подхода. В отличие от классической sales funnel, представленные алгоритмы позволяют использовать многомерную conversion funnel не только для оценки результатов работы бизнеса за отчетный период: благодаря потоку аргументов модели в режиме реального времени становится возможным оптимизировать коммерческий процесс за счет перехода к концепции опережающих экономических показателей.На практике это означает возможность реализации на цифровых платформах эффективного планирования коммерческой деятельности. Аргументами математической модели служат интернет-статистика, динамика потребительских предпочтений, история бизнес-процесса, аккумулированная в системе больших данных. При этом задействованы средства queuing theory, дифференциального исчисления, экономико-математического моделирования с опорой на такие показатели, как KPI (Key Performance Indicators), CTR (click-through rate), CR (Conversion rate). Это позволило сформулировать концепцию цифрового двойника коммерческого процесса. Нами разработаны математические формализмы, удобные для практических приложений. Это позволяет обеспечить приемлемую для программирования на ЭВМ реализацию алгоритмов, описывающих conversion funnel

Interaction of matter-wave gap solitons in optical lattices

We study mobility and interaction of gap solitons in a Bose-Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of discreteness imposed onto a BEC by the lattice potential. We show that inelastic collisions of two weakly localized near-the-band-edge gap solitons provide simple and effective means for generating strongly localized in-gap solitons through soliton fusion.Comment: 12 pages, 7 figure

Efficacy of Various Regimens of Inhibitor-Protected Penicillins on the Basis of Immunospecific Mixed Saliva Proteins in Patients after Dental Implantation: a Randomized Uncontrolled Trial

Background. The available comparative studies on issues of choosing antibiotic regimen in dental implantation are often observational and describe only visible postoperative signs. More objective assessment of postoperative period and comparison of approaches requires laboratory tests. One of the methods to be used at a dental appointment is to study examination of the biochemical properties of saliva.Objective. To carry out comparative evaluation of single and prolonged regimens of amoxicillin/clavulanate administration after dental implantation indicated by nonspecific immunity in mixed saliva.Methods. A randomized uncontrolled trial of 30 partially edentulous patients was conducted. The clinical phase of the study was performed at the Department of Propaedeutics of Surgical Dentistry, MSUMD; the laboratory phase — at the Pharmacology and Biological Chemistry Departments, MSUMD, in 2021–2022. The study included patients aged 18 to 75 years, anatomically suitable for dental implant placement. Patients with somatic diseases in the decompensation stage were excluded from the study. Patients were randomized into 2 groups. The group 1 was prescribed to take amoxicillin/clavulanate pills (875+125 mg) 30 minutes before surgery. The group 2 was to take amoxicillin/clavulanate (875+125 mg) 30 minutes before surgery and then 1 pill of Amoxicillin/ Clavulanate (500+125 mg) 2 times a day for 7 days after surgery. To evaluate the efficacy of the applied antibiotic therapy, unstimulated mixed saliva was collected from all patients on an empty stomach, 1 ml before surgery and on the third day after surgery. The amount of immunoglobulins of G, M, A classes (mg/l) and б-amylase activity (IU/l) were determined spectrophotometrically in the saliva samples. Statistical processing of laboratory data was performed using Welch's t-test by means of Statistica 10 Pro (StatSoft, USA). Intergroup and intragroup differences were considered significant at p ≤ 0.05.Results. Based on the saliva proteins examined, the most pronounced difference between the patient groups was obtained for IgA. For other studied parameters of saliva, no significant difference between the groups was obtained on the third day after the surgery. However, despite the absence of a statistical difference, a tendency to a stronger increase in the amount of IgA, G, IgM, salivary amylase activity was noted for all indicators; moreover, a high correlation between immunoglobulins of class A, G, immunoglobulins of class G, M, and immunoglobulins of class A, M was revealed.Conclusion. Among patients with the prolonged regimen, the groups did not differ significantly in such saliva parameters as immunoglobulins G and M and salivary б-amylase activity, however, a tendency to a stronger increase of the mentioned immunoglobulins in the saliva of group 1 patients was revealed. The most significant difference was recorded for immunoglobulin A in saliva, the amount of which was significantly lower in the group of prolonged antibiotic administration (p < 0.05)

Bose-Einstein Condensates in Optical Lattices: Band-Gap Structure and Solitons

We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions