Physics of randomness and regularities for cities, languages, and their lifetimes and family trees

Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size distribution of the cities and for that of the languages, respectively. The cities and the languages are treated differently (and as connected; for example, the languages split in terms of splitting the cities, etc.) and thus two distributions are obtained in the same computation at the same time. Evolutions of lifetimes and families for the cities and the languages are also studied. We suggest that the regularities may be evolving out of randomness, in terms of the relevant processes.Comment: 22 pages including all figures; for Int. J. Mod. Phys. C 18 (2007

Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Tanısal ikileme neden olan apandikolitiyazis: Akut apandisitin nadir görülen bir sebebi (Olgu sunumu)

Appendicolithiasis is a condition characterized by a concretion in the vermiform appendix. Appendicoliths are found in 10% of patients with acute appendicitis, but they are seen more frequently in perforated appendicitis and in abscess formation. We herein report a case of acute appendicitis due to appendicolithiasis, which mimics acute disorders of the genitourinary tract and causes diagnostic confusion. A 38-year-old man presented to our emergency department with a history of intense, acute, recurrent, crampy right lower quadrant pain radiating to the right groin region, accompanied by nausea. Physical examination revealed muscular defense and rebound tenderness in the right lower quadrant, tenderness in the line of the right ureter and right costovertebral angle tenderness. On X-ray examination, a right kidney stone was identified as was an incidental 3-cm density in the right lower quadrant. The patient underwent appendectomy. The diagnosis was made by operation and also X-ray examination of the appendectomy material showing appendicolithiasis. Acute appendicitis may manifest as a variety of genitourinary disorders. The possibility of an appendicolith with or without acute appendicitis must always be considered in the differential diagnosis of acute lower abdominal and pelvic disorders, and in the consideration of common acute urological disorders

Система управління оборотним капіталом підприємства: елементна структура та ефектівність

Метою дослідження є створення комплексної сістеми менеджменту оборотним капіталом та забезпечення її ефективного функціонування. В цьому зв’язку необхідно управляти не лише окремими елементами оборотного капіталу, але і всіма бізнес – процесами підприємства з інтегруванням у стратегічне управління. Це зумовлено тим, що систему управління оборотним капіталом не доцільно розглядати відокремлено від всього підприємства, а її варто досліджувати у комплексі з іншими підсистемами

Time evolution of the scattering data for a fourth-order linear differential operator

The time evolution of the scattering and spectral data is obtained for the differential operator $\displaystyle\frac{d^4}{dx^4} +\displaystyle\frac{d}{dx} u(x,t)\displaystyle\frac{d}{dx}+v(x,t),$ where $u(x,t)$ and $v(x,t)$ are real-valued potentials decaying exponentially as $x\to\pm\infty$ at each fixed $t.$ The result is relevant in a crucial step of the inverse scattering transform method that is used in solving the initial-value problem for a pair of coupled nonlinear partial differential equations satisfied by $u(x,t)$ and $v(x,t).$Comment: 19 page

Assessment of Dynamic Change of Coronary Artery Geometry and Its Relationship to Coronary Artery Disease, Based on Coronary CT Angiography

To investigate the relationship between dynamic changes of coronary artery geometry and coronary artery disease (CAD) using computed tomography (CT). Seventy-one patients underwent coronary CT angiography with retrospective electrocardiographic gating. End-systolic (ES) and end-diastolic (ED) phases were automatically determined by dedicated software. Centerlines were extracted for the right and left coronary artery. Differences between ES and ED curvature and tortuosity were determined. Associations of change in geometrical parameters with plaque types and degree of stenosis were investigated using linear mixed models. The differences in number of inflection points were analyzed using Wilcoxon signed-rank tests. Tests were done on artery and segment level. One hundred thirty-seven arteries (64.3%) and 456 (71.4%) segments were included. Curvature was significantly higher in ES than in ED phase for arteries (p = 0.002) and segments (p < 0.001). The difference was significant only at segment level for tortuosity (p = 0.005). Number of inflection points was significantly higher in ES phase on both artery and segment level (p < 0.001). No significant relationships were found between degree of stenosis and plaque types and dynamic change in geometrical parameters. Non-invasive imaging by cardiac CT can quantify change in geometrical parameters of the coronary arteries during the cardiac cycle. Dynamic change of vessel geometry through the cardiac cycle was not found to be related to the presence of CAD

Explicit solutions to the Korteweg-de Vries equation on the half line

Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.Comment: 17 pages, no figure

Electroactive nanoinjection platform for intracellular delivery and gene silencing

Background: Nanoinjection—the process of intracellular delivery using vertically configured nanostructures—is a physical route that efficiently negotiates the plasma membrane, with minimal perturbation and toxicity to the cells. Nanoinjection, as a physical membrane-disruption-mediated approach, overcomes challenges associated with conventional carrier-mediated approaches such as safety issues (with viral carriers), genotoxicity, limited packaging capacity, low levels of endosomal escape, and poor versatility for cell and cargo types. Yet, despite the implementation of nanoinjection tools and their assisted analogues in diverse cellular manipulations, there are still substantial challenges in harnessing these platforms to gain access into cell interiors with much greater precision without damaging the cell’s intricate structure. Here, we propose a non-viral, low-voltage, and reusable electroactive nanoinjection (ENI) platform based on vertically configured conductive nanotubes (NTs) that allows for rapid influx of targeted biomolecular cargos into the intracellular environment, and for successful gene silencing. The localization of electric fields at the tight interface between conductive NTs and the cell membrane drastically lowers the voltage required for cargo delivery into the cells, from kilovolts (for bulk electroporation) to only ≤ 10 V; this enhances the fine control over membrane disruption and mitigates the problem of high cell mortality experienced by conventional electroporation. Results: Through both theoretical simulations and experiments, we demonstrate the capability of the ENI platform to locally perforate GPE-86 mouse fibroblast cells and efficiently inject a diverse range of membrane-impermeable biomolecules with efficacy of 62.5% (antibody), 55.5% (mRNA), and 51.8% (plasmid DNA), with minimal impact on cells’ viability post nanoscale-EP (> 90%). We also show gene silencing through the delivery of siRNA that targets TRIOBP, yielding gene knockdown efficiency of 41.3%. Conclusions: We anticipate that our non-viral and low-voltage ENI platform is set to offer a new safe path to intracellular delivery with broader selection of cargo and cell types, and will open opportunities for advanced ex vivo cell engineering and gene silencing. Graphical abstract: [Figure not available: see fulltext.

Exact solutions to the focusing nonlinear Schrodinger equation

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form in terms of matrix exponentials. Such exact solutions can alternatively be written explicitly as algebraic combinations of exponential, trigonometric, and polynomial functions of the spatial and temporal coordinates.Comment: 60 pages, 18 figure

Multiscale Theory of Finite Size Bose Systems: Implications for Collective and Single-Particle Excitations

Boson droplets (i.e., dense assemblies of bosons at low temperature) are shown to mask a significant amount of single-particle behavior and to manifest collective, droplet-wide excitations. To investigate the balance between single-particle and collective behavior, solutions to the wave equation for a finite size Bose system are constructed in the limit where the ratio \varepsilon of the average nearest-neighbor boson distance to the size of the droplet or the wavelength of density disturbances is small. In this limit, the lowest order wave function varies smoothly across the system, i.e., is devoid of structure on the scale of the average nearest-neighbor distance. The amplitude of short range structure in the wave function is shown to vanish as a power of \varepsilon when the interatomic forces are relatively weak. However, there is residual short range structure that increases with the strength of interatomic forces. While the multiscale approach is applied to boson droplets, the methodology is applicable to any finite size bose system and is shown to be more direct than field theoretic methods. Conclusions for Helium-4 nanodroplets are drawn.Comment: 28 pages, 5 figure