Homological smoothness and deformations of generalized Weyl algebras

It is an immediate conclusion from Bavula's papers \cite{Bavula:GWA-def}, \cite{Bavula:GWA-tensor-product} that if a generalized Weyl algebra A=\kk[z;\lambda,\eta,\varphi(z)] is homologically smooth, then the polynomial $\varphi(z)$ has no multiple roots. We prove in this paper that the converse is also true. Moreover, formal deformations of $A$ are studied when \kk is of characteristic zero.Comment: Final version, 36 page

Non-commutative deformations and quasi-coherent modules

We identify a class of "quasi-compact semi-separated" (qcss) twisted presheaves of algebras A for which well-behaved Grothendieck abelian categories of quasi-coherent modules Qch(A) are defined. This class is stable under algebraic deformation, giving rise to a 1-1 correspondence between algebraic deformations of A and abelian deformations of Qch(A). For a qcss presheaf A, we use the Gerstenhaber-Schack (GS) complex to explicitely parameterize the first order deformations. For a twisted presheaf A with central twists, we descibe an alternative category QPr(A) of quasi-coherent presheaves which is equivalent to Qch(A), leading to an alternative, equivalent association of abelian deformations to GS cocycles of qcss presheaves of commutative algebras. Our construction applies to the restriction O of the structure sheaf of a scheme X to a finite semi-separating open affine cover (for which we have an equivalence between Qch(O) and Qch(X)). Under a natural identification of Gerstenhaber-Schack cohomology of O and Hochschild cohomology of X, our construction is shown to be equivalent to Toda's construction in the smooth case

Deterministic Separation of Cancer Cells from Blood at 10 mL/min

Circulating tumor cells (CTCs) and circulating clusters of cancer and stromal cells have been identified in the blood of patients with malignant cancer and can be used as a diagnostic for disease severity, assess the efficacy of different treatment strategies and possibly determine the eventual location of metastatic invasions for possible treatment. There is thus a critical need to isolate, propagate and characterize viable CTCs and clusters. Here, we present a microfluidic device for mL/min flow rate, continuous-flow capture of viable CTCs from blood using deterministic lateral displacement arrays. We show here that a deterministic bump array can be designed such that it will isolate with efficiency greater than 85% CTCs over a large range in sizes from millimeter volume clinical blood samples in minutes, with no effect on cell vitality so that further culturing and analysis of the cells can be carried out

Modeling Three-dimensional Invasive Solid Tumor Growth in Heterogeneous Microenvironment under Chemotherapy

A systematic understanding of the evolution and growth dynamics of invasive solid tumors in response to different chemotherapy strategies is crucial for the development of individually optimized oncotherapy. Here, we develop a hybrid three-dimensional (3D) computational model that integrates pharmacokinetic model, continuum diffusion-reaction model and discrete cell automaton model to investigate 3D invasive solid tumor growth in heterogeneous microenvironment under chemotherapy. Specifically, we consider the effects of heterogeneous environment on drug diffusion, tumor growth, invasion and the drug-tumor interaction on individual cell level. We employ the hybrid model to investigate the evolution and growth dynamics of avascular invasive solid tumors under different chemotherapy strategies. Our simulations reproduce the well-established observation that constant dosing is generally more effective in suppressing primary tumor growth than periodic dosing, due to the resulting continuous high drug concentration. In highly heterogeneous microenvironment, the malignancy of the tumor is significantly enhanced, leading to inefficiency of chemotherapies. The effects of geometrically-confined microenvironment and non-uniform drug dosing are also investigated. Our computational model, when supplemented with sufficient clinical data, could eventually lead to the development of efficient in silico tools for prognosis and treatment strategy optimization.Comment: 41 pages, 8 figure

Аванпроєкт пасажирського дальньо-магістрального літака місткістю 240 пасажирів

Робота публікується згідно наказу Ректора НАУ від 27.05.2021 р. №311/од "Про розміщення кваліфікаційних робіт здобувачів вищої освіти в репозиторії університету". Керівник роботи: професор, д.т.н. Карускевич Михайло ВіталійовичThis diploma work is dedicated to preliminary design of the long-range passenger aircraft with 240 passengers capacity and its design characteristic estimation. The work considers comparative analyze of the planes-prototypes and selection of the most advanced technical decisions for wing, fuselage, tail unit, landing gear, high lift devices, primary flight control surfaces. For the acceptable range of center of gravity position the iterative method for the units mass location have been used. The diploma work contains preliminary design of the Roller Module for cargo hold and container compartment in the special part.Дана дипломна робота присвячена ескізному проекту далекомагістрального пасажирського літака місткістю 240 пасажирів та оцінці його конструктивних характеристик. У роботі розглянуто порівняльний аналіз літаків-прототипів і вибір найбільш прогресивних технічних рішень крила, фюзеляжу, хвостового оперення, шасі, підйомної сили, основних поверхонь управління польотом. Для прийнятного діапазону положення центру ваги використовувався ітераційний метод визначення маси одиниць. У дипломній роботі наведено ескізний проект роликового модуля вантажного трюму та контейнерного відсіку в спеціальній частині