An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise

Logistic growth models are recurrent in biology, epidemiology, market models, and neural and social networks. They find important applications in many other fields including laser modelling. In numerous realistic cases the growth rate undergoes stochastic fluctuations and we consider a growth model with a stochastic growth rate modelled via an asymmetric Markovian dichotomic noise. We find an exact analytical solution for the probability distribution providing a powerful tool with applications ranging from biology to astrophysics and laser physics

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

The Measure of the Orthogonal Polynomials Related to Fibonacci Chains: The Periodic Case

The spectral measure for the two families of orthogonal polynomial systems related to periodic chains with N-particle elementary unit and nearest neighbour harmonic interaction is computed using two different methods. The interest is in the orthogonal polynomials related to Fibonacci chains in the periodic approximation. The relation of the measure to appropriately defined Green's functions is established.Comment: 19 pages, TeX, 3 scanned figures, uuencoded file, original figures on request, some misprints corrected, tbp: J. Phys.

Field Evaluation of Highly Insulating Windows in the Lab Homes: Winter Experiment

This field evaluation of highly insulating windows was undertaken in a matched pair of 'Lab Homes' located on the Pacific Northwest National Laboratory (PNNL) campus during the 2012 winter heating season. Improving the insulation and solar heat gain characteristics of a home's windows has the potential to significantly improve the home's building envelope and overall thermal performance by reducing heat loss (in the winter), and cooling loss and solar heat gain (in the summer) through the windows. A high quality installation and/or window retrofit will also minimize or reduce air leakage through the window cavity and thus also contribute to reduced heat loss in the winter and cooling loss in the summer. These improvements all contribute to decreasing overall annual home energy use. Occupant comfort (non-quantifiable) can also be increased by minimizing or eliminating the cold 'draft' (temperature) many residents experience at or near window surfaces that are at a noticeably lower temperature than the room air temperature. Lastly, although not measured in this experiment, highly insulating windows (triple-pane in this experiment) also have the potential to significantly reduce the noise transmittance through windows compared to standard double-pane windows. The metered data taken in the Lab Homes and data analysis presented here represent 70 days of data taken during the 2012 heating season. As such, the savings from highly insulating windows in the experimental home (Lab Home B) compared to the standard double-pane clear glass windows in the baseline home (Lab Home A) are only a portion of the energy savings expected from a year-long experiment that would include a cooling season. The cooling season experiment will take place in the homes in the summer of 2012, and results of that experiment will be reported in a subsequent report available to all stakeholders

Field Evaluation of Highly Insulating Windows in the Lab Homes: Winter Experiment

This field evaluation of highly insulating windows was undertaken in a matched pair of 'Lab Homes' located on the Pacific Northwest National Laboratory (PNNL) campus during the 2012 winter heating season. Improving the insulation and solar heat gain characteristics of a home's windows has the potential to significantly improve the home's building envelope and overall thermal performance by reducing heat loss (in the winter), and cooling loss and solar heat gain (in the summer) through the windows. A high quality installation and/or window retrofit will also minimize or reduce air leakage through the window cavity and thus also contribute to reduced heat loss in the winter and cooling loss in the summer. These improvements all contribute to decreasing overall annual home energy use. Occupant comfort (non-quantifiable) can also be increased by minimizing or eliminating the cold 'draft' (temperature) many residents experience at or near window surfaces that are at a noticeably lower temperature than the room air temperature. Lastly, although not measured in this experiment, highly insulating windows (triple-pane in this experiment) also have the potential to significantly reduce the noise transmittance through windows compared to standard double-pane windows. The metered data taken in the Lab Homes and data analysis presented here represent 70 days of data taken during the 2012 heating season. As such, the savings from highly insulating windows in the experimental home (Lab Home B) compared to the standard double-pane clear glass windows in the baseline home (Lab Home A) are only a portion of the energy savings expected from a year-long experiment that would include a cooling season. The cooling season experiment will take place in the homes in the summer of 2012, and results of that experiment will be reported in a subsequent report available to all stakeholders

Anomalously large oxygen-ordering contribution to the thermal expansion of untwinned YBa2Cu3O6.95 single crystals: a glass-like transition near room temperature

We present high-resolution capacitance dilatometry studies from 5 - 500 K of untwinned YBa2Cu3Ox (Y123) single crystals for x ~ 6.95 and x = 7.0. Large contributions to the thermal expansivities due to O-ordering are found for x ~ 6.95, which disappear below a kinetic glass-like transition near room temperature. The kinetics at this glass transition is governed by an energy barrier of 0.98 +- 0.07 eV, in very good agreement with other O-ordering studies. Using thermodynamic arguments, we show that O-ordering in the Y123 system is particularly sensitive to uniaxial pressure (stress) along the chain axis and that the lack of well-ordered chains in Nd123 and La123 is most likely a consequence of a chemical-pressure effect.Comment: 4 pages, 3 figures, submitted to PR

Some Orthogonal Polynomials Arising from Coherent States

We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known orthogonal polynomials but in many cases we encounter a general class of new orthogonal polynomials for which we establish several qualitative results.Comment: 21 page

NUMERIČKO INTEGRIRANJE KOD IZRAČUNA VOLUMENA NEPRAVILNIH ANTIKLINALA

The volume of geological structures is often calculated by using the definite integral. Though in some cases the integral can be solved analytically, in practice we usually approximate its value by numerical integration techniques. The application of definite integral in volume calculation is illustrated by two examples. The volume of Mount Fuji, the world-known “conic” geomorphological structure, is calculated by analytical integration. Two basic numerical integration methods, that is, the trapezoidal and Simpson’s rule are applied to subsurface hydrocarbon reservoir volume calculation, where irregular anticline is approximated by a frustum of a right circular cone.Pri izračunavanju volumena geoloških struktura često se koristi određeni integral. Iako se u nekim slučajevima integral može riješiti analitički, u praksi se njegova vrijednost obično procjenjuje koristeći tehnike numeričke integracije. Primjena određenog integrala u izračunavanju volumena ilustrirana je dvama primjerima. Volumen planine Fuji, koja je svjetski poznati geomorfološki primjer “stožaste” strukture, izračunat je analitičkom integracijom. Dvije temeljne metode numeričkog integriranja, tj. trapezno i Simpsonovo pravilo, primijenjene su na izračun volumena ležišta ugljikovodika, gdje je struktura nepravilne antiklinale aproksimirana pravilnim krnjim stošcem

Infrared and optical properties of pure and cobalt-doped LuNi_2B_2C

We present optical conductivity data for Lu(Ni$_{1-x}$Co$_x$)$_2$B$_2$C over a wide range of frequencies and temperatures for x=0 and x=0.09. Both materials show evidence of being good Drude metals with the infrared data in reasonable agreement with dc resistivity measurements at low frequencies. An absorption threshold is seen at approximately 700 cm-1. In the cobalt-doped material we see a superconducting gap in the conductivity spectrum with an absorption onset at 24 +/- 2 cm-1 = 3.9$ +/- 0.4 k_BT_c suggestive of weak to moderately strong coupling. The pure material is in the clean limit and no gap can be seen. We discuss the data in terms of the electron-phonon interaction and find that it can be fit below 600 cm-1 with a plasma frequency of 3.3 eV and an electron-phonon coupling constant lambda_{tr}=0.33 using an alpha^{2}F(omega) spectrum fit to the resistivity.Comment: 10 pages with 10 embedded figures, submitted to PR