Function generator has been widely used in each electronics fields recent years. In this thesis, the authors will introduce some basic structure and working principles of a function generator, moreover a function generator which can create three kinds of wave: sine wave, square wave and triangle wave has been implemented. There are many ways to build the function generator; a method of combine the operational amplifier and discrete components is introduced in this thesis. First use the RC Wien bridge oscillator to achieve sinusoidal wave; and convert it into square wave by using the shaping circuit. Lastly, use the integrating circuit to obtain triangle wave. The basic simulation software Multisim has been used to simulate the circuit.

The function $sin x$ as one of the six trigonometric functions is fundamental in nearly every branch of mathematics, and its applications. In this thesis, we study an integral equation related to that of $sin x$: $mbox{~for~}xin[-frac{hat{pi}_{p}}{2},~frac{hat{pi}_{p}}{2}] mbox{~and~} p>1$ $$x=int_0^{S_{p}(x)}(1-|t|^{p})^{-frac{1}{p}}dt.$$ Here $hat{pi}_{p}=frac{2pi}{psin(frac{pi}{p})}=2int_0^1(1-t^{p})^{-frac{1}{p}}dt.$ We find that the function $S_{p}(x)$ is well defined. Its properties are also similar to those of $sin x$ : differentiation, identities, periodicity, asymptotic expansions, $cdots$, etc. For example, we have $$|S_{p}(x)|^{p}+|S'_{p}(x)|^{p}=1mbox{~~and~~}frac{d}{dx}(|S'_{p}(x)|^{p-2}S'_{p}(x))=-(p-1)|S_{p}(x)|^{p-2}S_{p}(x).$$ We call $S_{p}(x)$ the generalized sine function. Similarly, we define the generalized cosine function $C_{p}(x)$ by $|x|=int_{C_{p}(x)}^{1}(1- t^{p})^{-frac{1}{p}}dt$ for $xin[-frac{hat{pi}_{p}}{2}$,~$frac{hat{pi}_{p}}{2}]$ and derive its properties. Thus we obtain two sets of trigonometric functions: egin{itemize} item[(i)]$~S_{p}(x),~ S'_{p}(x),~ T_{p}(x)=frac{S_{p}(x)}{S'_{p}(x)},~RT_{p}(x)=frac{S'_{p}(x)}{S_{p}(x)},~ SE_{p}(x)=frac{1}{S'_{p}(x)},~ RS_{p}(x)=frac{1}{S_{p}(x)}~;$ item[(ii)]$~C_{p}(x),~ C'_{p}(x),~RCT_{p}(x)=-frac{C'_{p}(x)}{C_{p}(x)},~ CT_{p}(x)=-frac{C_{p}(x)}{C'_{p}(x)},~RC_{p}(x)=frac{1}{C_{p}(x)},~ CS_{p}(x)=-frac{1}{C'_{p}(x)}mbox{~¡C~}$ end{itemize}These two sets of functions have similar differentiation formulas, identities and periodic properties as the classical trigonometric functions. They coincide when $p=2$. Their graphs and asymptotic expansions are also interesting. Through this study, we understand more about the theoretical framework of trigonometric functions.

Whole genome sequencing (WGS) projects for model mammalian organisms exposed the magnitude to which transposable elements (TEs) have contributed to DNA content, but led to inferences on repeat composition and activity patterns which do not capture the true diversity within Mammalia. Understanding of the evolutionary importance of TEs and the development of TEs for biological applications are hindered when considering only the data gathered from a limited sampling of model organisms. The research presented here begins with analysis of a mouse lemur WGS dataset, revealing an exception in the primate lineage to the generalizations garnered from model organisms. A recently active TE was uncovered with evidence of horizontal transfer involving a primate and another mammal; this discovery may lead to a useful transfection vector with known efficacy in mammalian cells. Furthermore, an opportunity to observe atypical patterns of TE diversification within a mammalian family was achieved through survey sequencing and comparative analyses of five vespertilionid taxa and a phyllostomid outgroup. A potential inverse relationship between the two classes of TEs was tentatively described, and further explored by an in-depth analysis of the dominant TE family from each class in a species with WGS data available. The interplay of the two classes could not previously be investigated in mammals, due to ~40 million years of Class II TE inactivity in model organisms. Through exploration of activity patterns of both classes, this study provides insight on the relationship between TEs and their host.

No description available.

This thesis discusses the Ruijsenaars-Schneider model and its connection to Calogero-Moser systems and the sine-Gordon equation. The derivations and mathematical framework presented aims at making the model comprehensible to non-experts in the field. Two different methods, the Bäcklund transformation and Ruijsenaars-Schneider model, are used to find soliton solutions to the sine-Gordon equation.

The goal of this Thesis is to give a presentation of some key issues regarding the non-perturbative renormalization of the periodic scalar field theories. As an example of the non-perturbative methods, we use the differential renormalization group approach, particularly the Wegner-Houghton and the Polchinski renormalization group equations, in order to investigate the renormalization of a one-component periodic scalar field theory. The Wegner-Houghton equation provides a resummation of the loop-expansion, and the Polchinski equation is based on the resummation of the perturbation series. Therefore, these equations are exact in the sense that they contain all quantum corrections. In the framework of these renormalization group equations, field theories with periodic self interaction can be considered without violating the essential symmetry of the model: the periodicity. Both methods - the Wegner-Houghton and the Polchinski approaches - are inspired by Wilson's blocking construction in momentum space: the Wegner-Houghton method uses a sharp momentum cut-off and thus cannot be applied directly to non-constant fields (contradicts with the "derivative expansion"); the Polchinski method is based on a smooth cut-off and thus gives rise naturally to a "derivative expansion" for varying fields. However, the shape of the cut-off function (the "scheme") is not fixed a priori within Polchinski's ansatz. In this thesis, we compare the Wegner--Houghton and the Polchinski equation; we demonstrate the consistency of both methods for near-constant fields in the linearized level and obtain constraints on the regulator function that enters into Polchinski's equation. Analytic and numerical results are presented which illustrate the renormalization group flow for both methods. We also briefly discuss the relation of the momentum-space methods to real-space renormalization group approaches. For the two-dimensional Coulomb gas (which is investigated by a real-space renormalization group method using the dilute-gas approximation), we provide a systematic method for obtaining higher-order corrections to the dilute gas result.

Investigamos a existência de uma fase de Kosterlitz-Thouless no estado fundamentai de um sistema de rotores quânticos em uma dimensão. Provamos que o modelo não exibe uma transição de primeira ordem, já que a estimativa de McBryan-Spencer é válida para os rotores. Obtemos a função de partição do modelo nas representações de Lie-Trotter, de sine-Gordon, e na representação das cargas. Nessa última, provamos um limite inferior para a função de correlação entre cargas externas. Ainda na representação das cargas, damos uma nova prova do decaimento polinomial do limite superior para a função de correlação de um gás de dipolos (caroço duro) na presença de cargas externas. / We investigate the existence of a Kosterlitz-Thoules phase in the ground state of a one-dimensional array of quantum rotators. We prove that this model does not exhibit a first-order phase transition since a McBryan-Spencer bound holds for it. We obtain the partition function of the rotators in the Lie-Trotter, sine-Gordon, and charge representations. In this latter representation, we give a new proof of the upper bound polynomial decay on the external charges correlation function of a dipole gas with hardcore.

Išsilaisvinus iš sovietų okupacijos, Lietuvos įstatymų leidėjai į šalies teisinę sistemą inkorporavo konvencijos Dėl kelio užkirtimo genocido nusikaltimui ir baudimo už jį nuostatas. Be to, siekiant nubausti asmenis, kaltus už okupacijos metu vykdytus nusikaltimus, į genocido apibrėžimą buvo įtrauktos taip pat politinės bei socialinės grupės. Tačiau toks Lietuvos įstatymų leidėjų žingsnis praplėtė tarptautinėje teisėje įtvirtintą genocido apibrėžimą, kuriame numatoma, jog genocidu siekiama visiškai ar iš dalies sunaikinti nacionalinę, etninę, rasinę ar religinę grupę, taigi ne politinę ar socialinę grupę. Pagal tarptautinės teisės principą nullum crimen sine lege niekas negali būti baudžiamas už nusikaltimą, kuris jo darymo metu nebuvo draudžiamas įstatymu. Šiame darbe siekiama nustatyti ar Lietuvos teisinėje sistemoje įtvtirtintas išplėstinis genocido sudėties apibrėžimas nepažeidžia principo nullum crimen sine lege. Darbą sudaro trys pagrindinės dalys, kuriose atskleidžiami nagrinėjamos problemos teoriniai bei praktiniai aspektai. Pirmojoje dalyje nagrinėjamas genocido apibrėžimas, priežastys kodėl politinės ir socialinės grupės nebuvo įtrauktos į Genocido konvenciją bei analizuojama kitų šalių praktika apibrėžiant genocido veiką. Politinės ir socialinės grupės į konvenciją nebuvo įtrauktos dėl politinių priežasčių, iškilus tam tikrų šalių prieštaravimams. Tačiau Lietuva ne vienintelė įtraukė šias grupes į savo įstatymus, tai rodo, kad ne vien Lietuvai svarbi šių grupių... [toliau žr. visą tekstą] / Genocide is described as one of the most severe crimes of the international law. After the Second World War international community decided to codify international law and the general principles of the law recognized by civilized nations. The United Nations enacted The Convention on the Prevention and Punishment of the Crime of Genocide. The convention stated that genocide crime is described as acts against national, ethnic, racial or religious group. After the collapse of the Soviet Union, many countries including Lithuania got back their independence. Lithuania’s legislators incorporated the norms of the Genocide convention into the state’s legal system. Besides these norms legislators also included social and political groups into the definition of genocide crime. It was done in order to punish persons, who were responsible for the criminal offense against Lithuania’s citizen during soviet occupation. The decision that states legislators made extended the definition of genocide crime established in international law, which defines genocide as the acts against national, ethnic, racial or religious group, but not against social or political group. Under international principle nullum crimen sine lege a person should not face criminal punishment except for an act that was criminalized by law before he performed the act. In this work it is aimed to determine whether the extended genocide structure established in Lithuanian legal system does not violate principle nullum... [to full text]

Submitted by Simone Souza (simonecgsouza@hotmail.com) on 2018-04-20T15:11:04Z No. of bitstreams: 1 DISS_2014_Leonides da Rocha Mota.pdf: 1237393 bytes, checksum: 143ba9211bb27429e5a7a12c52f58839 (MD5) / Approved for entry into archive by Jordan (jordanbiblio@gmail.com) on 2018-05-14T16:48:32Z (GMT) No. of bitstreams: 1 DISS_2014_Leonides da Rocha Mota.pdf: 1237393 bytes, checksum: 143ba9211bb27429e5a7a12c52f58839 (MD5) / Made available in DSpace on 2018-05-14T16:48:32Z (GMT). No. of bitstreams: 1 DISS_2014_Leonides da Rocha Mota.pdf: 1237393 bytes, checksum: 143ba9211bb27429e5a7a12c52f58839 (MD5) Previous issue date: 2014-02-07 / CAPES / Neste trabalho, examinamos a integrabilidade do modelo generalizado de sine-Gordon (GsG), no contexto do teste de Painlevé para equações diferenciais parciais (EDPs). Mostramos que o modelo (GsG) possui certos submodelos como o modelo duplo sine-Gordon (DsG), Bukhvostov-Lipatov (BL) e os modelos integráveis sine-Gordon. O modelo BL possui algumas direções integráveis no espaço dos campos. Classi camos as massas das soluções tipo sólitons (kinks) do modelo (GsG) através dos pesos máximos da álgebra de Lie sl(3), e mostramos que essas massas pertencem a determinados multipletos neste esquema de representação. Abordamos o modelo integrável NLS defocusing e estudamos a colisão de dois sólitons dark, em particular estudamos a mudança de fase após a sua colisão. / In this work the integrability of the generalized sine-Gordon model (GsG) is examined in the context of the Painlevé test for partial di erential equations (PDEs). We show that the (GsG) model possesses certain submodels such as the double sine-Gordon (DsG), Bukhvostov-Lipatov (BL) and the integrable sine-Gordon models. The BL model possesses some integrable directions in the eld space. Moreover, we classify the kink type solutions of the (GsG) model through the highest weight representations of the underlying sl(3) Lie algebra, and we show that these masses belong to certain multiplets in that representation scheme. We discussed the integrable defocusing NLS model and study the collision of two dark solitons, in particular we study the phase shift after their collision.

Investigamos a existência de uma fase de Kosterlitz-Thouless no estado fundamentai de um sistema de rotores quânticos em uma dimensão. Provamos que o modelo não exibe uma transição de primeira ordem, já que a estimativa de McBryan-Spencer é válida para os rotores. Obtemos a função de partição do modelo nas representações de Lie-Trotter, de sine-Gordon, e na representação das cargas. Nessa última, provamos um limite inferior para a função de correlação entre cargas externas. Ainda na representação das cargas, damos uma nova prova do decaimento polinomial do limite superior para a função de correlação de um gás de dipolos (caroço duro) na presença de cargas externas. / We investigate the existence of a Kosterlitz-Thoules phase in the ground state of a one-dimensional array of quantum rotators. We prove that this model does not exhibit a first-order phase transition since a McBryan-Spencer bound holds for it. We obtain the partition function of the rotators in the Lie-Trotter, sine-Gordon, and charge representations. In this latter representation, we give a new proof of the upper bound polynomial decay on the external charges correlation function of a dipole gas with hardcore.