1,384 research outputs found

    A Few Things Differently

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    Focal Green's functions for fourth-order differential equations

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    Falling Vine Winery

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    For the past year or so, I have taken a class in vinification and worked in the beverage industry. I have discovered a great love for wine. I have immersed myself in the complicated process of vinification. For me art, architecture, and wine go hand in hand. There are many things we as Architects can draw from the process of vinification. I chose a location in southeast Minnesota, the site is fifteen miles from the city of Taylor's Falls. Taylor's Falls is a small community on the St. Croix river, with a population under one thousand people. Taylor's Falls is forty-five miles from the Twin Cities and just across the river from Wisconsin. The client for this project will be Hal Gershman, owner of four Happy Harry's bottle shops in Fargo and Grand Forks. Hal is also the president of the North American Wine Guild. The region of southeast Minnesota is developing as a legitimate wine growing area. The problem being, the area lacks the economic support to develop large scale wineries that produce enough wine to ship to other areas of the country. With developing a vineyard and winery that are capable of producing wine to serve the whole state and country, Minnesota will come to the forefront of U.S. wine making. By also opening a restaurant and wine bar, the income from the restaurant and wine bar will compensate for the winery until grape production is at its peak

    The Spiders of South Dakota

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    Spiders constitute the order of Araneida, which is one of the principal divisions of the class Arachnida. The Arachnida also includes scorpions, whipscorpions, pseudosscorpions, harvestmen, mites, and ticks. Some of the distinguishing characteristics of the Araneida are as follows: The head and thorax are consolidated into a cephalothorax. The abdomen is unsegmented and joined to the cephalothorax by a short narrow stalk. There are six pairs of appendages on the cephalothorax: chelicerae, pedipalps with heir basal masticulatory endites, and four pairs of walking legs

    The Spectrum of Crab Nebula X-Rays to 120 Kev

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    Counting rate and pulse height distribution spectral data of Crab Nebula telemetered from balloon detector

    Comparison theorems and asymptotic behavior of solutions of discrete fractional equations

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    Consider the following ν\nu-th order nabla and delta fractional difference equations \begin{equation} \begin{aligned} \nabla^\nu_{\rho(a)}x(t)&=c(t)x(t),\quad \quad t\in\mathbb{N}_{a+1},\\ x(a)&>0. \end{aligned}\tag{\ast} \end{equation} and \begin{equation} \begin{aligned} \Delta^\nu_{a+\nu-1}x(t)&=c(t)x(t+\nu-1),\quad \quad t\in\mathbb{N}_{a},\\ x(a+\nu-1)&>0. \end{aligned}\tag{\ast\ast} \end{equation} We establish comparison theorems by which we compare the solutions x(t)x(t) of (\ast) and (\ast\ast) with the solutions of the equations ρ(a)νx(t)=bx(t)\nabla^\nu_{\rho(a)}x(t)=bx(t) and Δa+ν1νx(t)=bx(t+ν1),\Delta^\nu_{a+\nu-1}x(t)=bx(t+\nu-1), respectively, where bb is a constant. We obtain four asymptotic results, one of them extends the recent result [F. M. Atici, P. W. Eloe, Rocky Mountain J. Math. 41(2011) 353--370]. These results show that the solutions of two fractional difference equations ρ(a)νx(t)=cx(t), 0<ν<1\nabla^\nu_{\rho(a)}x(t)=cx(t),\ 0<\nu<1, and Δa+ν1νx(t)=cx(t+ν1), 0<ν<1\Delta^\nu_{a+\nu-1}x(t)=cx(t+\nu-1),\ 0<\nu<1, have similar asymptotic behavior with the solutions of the first order difference equations x(t)=cx(t), c<1\nabla x(t)=cx(t),\ |c|<1 and Δx(t)=cx(t)\Delta x(t)=cx(t), c<1|c|<1 , respectively

    Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain

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    AbstractWe are concerned with proving existence of one or more than one positive solution of a general two point boundary value problem for the nonlinear equation Lx(t)≔−[p(t)xΔ(t)]Δ+q(t)xσ(t)=λa(t)f(t,xσ(t)). We shall also obtain criteria which leads to nonexistence of positive solutions. Here the independent variable t is in a “measure chain”. We will use fixed point theorems for operators on a Banach space
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