Continued Fractions with Multiple Limits

For integers $m \geq 2$, we study divergent continued fractions whose numerators and denominators in each of the $m$ arithmetic progressions modulo $m$ converge. Special cases give, among other things, an infinite sequence of divergence theorems, the first of which is the classical Stern-Stolz theorem. We give a theorem on a general class of Poincar{\'e} type recurrences which shows that they tend to limits when the limits are taken in residue classes and the roots of their characteristic polynomials are distinct roots of unity. We also generalize a curious $q$-continued fraction of Ramanujan's with three limits to a continued fraction with $k$ distinct limit points, $k\geq 2$. The $k$ limits are evaluated in terms of ratios of certain unusual $q$ series. Finally, we show how to use Daniel Bernoulli's continued fraction in an elementary way to create analytic continued fractions with $m$ limit points, for any positive integer $m \geq 2$.Comment: 29 pages. Updated/new conten

Utility, subjective probability, their interaction, and variance preferences

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66507/2/10.1177_002200276200600106.pd

Hamilton's principle: why is the integrated difference of kinetic and potential energy minimized?

I present an intuitive answer to an often asked question: why is the integrated difference K-U between the kinetic and potential energy the quantity to be minimized in Hamilton's principle? Using elementary arguments, I map the problem of finding the path of a moving particle connecting two points to that of finding the minimum potential energy of a static string. The mapping implies that the configuration of a non--stretchable string of variable tension corresponds to the spatial path dictated by the Principle of Least Action; that of a stretchable string in space-time is the one dictated by Hamilton's principle. This correspondence provides the answer to the question above: while a downward force curves the trajectory of a particle in the (x,t) plane downward, an upward force of the same magnitude stretches the string to the same configuration x(t).Comment: 7 pages, 4 figures. Submitted to the American Journal of Physic

Thermotectonic evolution of an extensional dome: the Cenozoic Osogovo-Lisets core complex (Kraishte zone, western Bulgaria)

The Kraishte region of Bulgaria is located at the junction of the Balkanides and Hellenides-Dinarides tectonic belts. Fission-track analysis on both apatites and zircons documents the Cenozoic exhumation of a Precambrian basement bounded by low-angle detachments. Late Eocene-Oligocene extension began prior to 47Ma and was dominantly in a top-to-the-southwest direction, confirmed by the sense of younging of apatite and zircon ages. This crustal extension controlled the formation of half-graben sedimentary basins on the hanging walls of the detachments. Thermal modelling of these hanging wall units provides evidence for heat transfer across the detachments from a relatively warm rising footwall. From 32 to 29Ma, pervasive magmatic activity resulted in the emplacement of rhyolitic to dacitic subvolcanic bodies and dykes, along with intrusion of the Osogovo granite. The results give evidence for extension in the southern Balkan older than, and separated from, the Miocene to Quaternary Aegean extension. This might reflect transtension during northeastward extrusion and rotation of continental fragments around the western boundary of Moesia. Eocene-Oligocene extension seems to have been controlled by the distribution of earlier thickening all around the Carpatho-Balkanic orocline, which is reflected by the Cretaceous emplacement of the Morava Nappe in the Kraisht

Active Mass Under Pressure

After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's theory might also be noticeable at the Newtonian level. A form of its surprising appearance, first noticed by Richard Chase Tolman, was discussed half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure

Immunotherapies and Metastatic Cancers: Understanding Utility and Predictivity of Human Immune Cell Engrafted Mice in Preclinical Drug Development

Metastases cause high mortality in several cancers and immunotherapies are expected to be effective in the prevention and treatment of metastatic disease. However, only a minority of patients benefit from immunotherapies. This creates a need for novel therapies that are efficacious regardless of the cancer types and metastatic environments they are growing in. Preclinical immuno-oncology models for studying metastases have long been limited to syngeneic or carcinogenesis-inducible models that have murine cancer and immune cells. However, the translational power of these models has been questioned. Interactions between tumor and immune cells are often species-specific and regulated by different cytokines in mice and humans. For increased translational power, mice engrafted with functional parts of human immune system have been developed. These humanized mice are utilized to advance understanding the role of immune cells in the metastatic process, but increasingly also to study the efficacy and safety of novel immunotherapies. From these aspects, this review will discuss the role of immune cells in the metastatic process and the utility of humanized mouse models in immuno-oncology research for metastatic cancers, covering several models from the perspective of efficacy and safety of immunotherapies

A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling

In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter- acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes

Galactoglucomannan-rich hemicellulose extract from Norway spruce (Picea abies) exerts beneficial effects on chronic prostatic inflammation and lower urinary tract symptoms in vivo

Galactoglucomannan (GGM) is the main hemicellulose class in wood of coniferous trees and could be potentially utilized as a possible health-promoting substance for food and pharmaceutical industry. Our aim was to evaluate effects of orally administered GGM-rich extract from Norway spruce in a rat model of chronic prostatitis associated with lower urinary tract symptoms (LUTS). Prostatic inflammation and LUTS was induced in male rats using testosterone and 17 beta-estradiol exposure for 18 weeks. Rats were treated with 2% GGM dissolved in drinking water during weeks 13-18. Pelvic pain response, LUT function and histopathological evaluation of the prostate were assessed. The results show that hormonal exposure induced LUTS seen as decreased urine flow rate, increased bladder pressure, voiding times, bladder capacity and residual urine volumes. GGM had positive effects on urodynamical parameters by decreasing the basal bladder pressure, increasing the urine flow rate and volume, reducing the residual volume and increasing micturition intervals. GGM reduced the extent of the hormone exposure-induced prostatic inflammation. Increase of pelvic pain induced by hormone exposure was only slightly affected by GGM treatment. The results suggest that orally administered GGM may have potential usage for improving lower urinary tract function associated with chronic prostatic inflammation. (C) 2017 Elsevier B.V. All rights reserved

Anomalous Behavior of the Contact Process with Aging

The effect of power-law aging on a contact process is studied by simulation and using a mean-field approach. We find that the system may approach its stationary state in a nontrivial, nonmonotonous way. For the particular value of the aging exponent, $\alpha=1$, we observe a rich set of behaviors: depending on the process parameters, the relaxation to the stationary state proceeds as $1/\ln t$ or via a power law with a nonuniversal exponent. Simulation results suggest that for $0<\alpha<1$, the absorbing-state phase transition is in the universality class of directed percolation.Comment: 4 pages revtex (twocolumn, psfig), 3 figure