Chebyshev polynomials and inequalities for Kleinian groups

The principal character of a representation of the free group of rank two into [Formula: see text] is a triple of complex numbers that determines an irreducible representation uniquely up to conjugacy. It is a central problem in the geometry of discrete groups and low dimensional topology to determine when such a triple represents a discrete group which is not virtually abelian, that is, a Kleinian group. A classical necessary condition is Jørgensen’s inequality. Here, we use certain shifted Chebyshev polynomials and trace identities to determine new families of such inequalities, some of which are best possible. The use of these polynomials also shows how we can identify the principal character of some important subgroups from that of the group itself.

Some Identities Involving Certain Hardy Sums and General Kloosterman Sums

Using the properties of Gauss sums, the orthogonality relation of character sum and the mean value of Dirichlet L-function, we obtain some exact computational formulas for the hybrid mean value involving general Kloosterman sums K ( r , l , λ ; p ) and certain Hardy sums S 1 ( h , q ) ∑ m = 1 p − 1 ∑ s = 1 p − 1 K ( m , n , λ ; p ) K ( s , t , λ ; p ) S 1 ( 2 m s ¯ , p ) , ∑ m = 1 p − 1 ∑ s = 1 p − 1 | K ( m , n , λ ; p ) | 2 | K ( s , t , λ ; p ) | 2 S 1 ( 2 m s ¯ , p ) . Our results not only cover the previous results, but also contain something quite new. Actually the previous authors just consider the case of the principal character λ modulo p, while we consider all the cases.

Marketing Strategies of Films in Bollywood Industry

This chapter examines the paradigm shift in the domain of marketing and promotion of Hindi cinema in the new millennium. The post-millennium Hindi film industry has resorted to the multimedia marketing of films with the incorporation of digital and social media marketing platforms as one of the key marketing strategies of contemporary Hindi cinema. Furthermore, in the modern scenario, release strategies such as saturated release and shorter release window have also become commonplace. The chapter elucidates on the impact of such practices on the narratives of Hindi cinema. It thereby considers the prevalence of high-concept style as the principal character is the trait of contemporary Bollywood cinema.

HEGEMONI DALAM NOVEL RONGGENG DUKUH PARUK KARYA AHMAD TOHARI

A literary work was an image of community social from a condition that is written and adds to it when once with an element of fiction. The social condition referred to include the structure, the system, of the people come from historical, including also the form of the hegemony of conducted by individuals or groups in those societies. This study aims to described the form of the hegemony of conducted by the main figure in the, srinthil, against other figures in a novel ronggeng dukuh paruk and the cause of the problem. The kind of research that is used is qualitative descriptive by using the hegemony of the theory. Research conducted in this research taken from the novel ronggeng dukuh paruk the work of ahmad tohari. The data collection using a technique been listening to and techniques recorded everything. While, data was undertaken analysis cycles reduction-analyze data-conclusion. The result of from the study states that found the form of and the causes of the hegemony of the principal character in a novel ronggeng dukuh paruk. The form of the hegemony of that leads to the stronghold of pharaoh matter.

Mimetic Desire in Dostoevsky’s The Idiot with Continual Reference to René Girard

It is common to see Myshkin, the principal character of Dostoevsky’s The Idiot, as a failed lover and a compassionate saintly figure, who gets entangled in a love triangle but cannot embody it. This paper challenges such a view and argues that Myshkin fully incarnates the violent dynamic of desire that governs the novel. With the help of René Girard’s notion of mimetic desire, the paper explores Myshkin’s relationship with Rogozhin as erotic rivalry. Instead of seeing the two characters as autonomous entities, it is suggested that they should be viewed as doubles, as two poles of the same consciousness. On this view, Myshkin’s compassion and Rogozhin’s lust become two different manifestations of the same desire, united by a conflict of interest, which drives the love triangle towards a violent resolution.

Domination inconscience (Id) du personnage principal dans le roman de Thérèse Raquin par Émile Zola

<p class="Abstract">This article talks about unconscious domination (Id) in the life of&nbsp;<span style="font-size: 1rem;">principal character in the novel Thérèse Raquin by Émile Zola,&nbsp;</span><span style="font-size: 1rem;">naturalist French writer. The method used in this research is&nbsp;</span><span style="font-size: 1rem;">qualitative method using structural theory and structural personality&nbsp;</span><span style="font-size: 1rem;">by Sigmund Freud. The result shows that there’s character&nbsp;</span><span style="font-size: 1rem;">development that utilize unconscious domination in Thérèse Raquin’s&nbsp;</span><span style="font-size: 1rem;">life. Thérèse’s unconscious domination had started since he met&nbsp;</span><span style="font-size: 1rem;">Laurent, motivated by her unequal ego since her childhood and&nbsp;</span><span style="font-size: 1rem;">Laurent’ influence that’s also controlled by Id since his school time.</span></p>

On large values of L(σ,χ)

In recent years, a variant of the resonance method was developed which allowed to obtain improved Ω-results for the Riemann zeta function along vertical lines in the critical strip. In the present paper, we show how this method can be adapted to prove the existence of large values of |L(σ,χ)| in the range σ∈(1/2,1], and to estimate the proportion of characters for which |L(σ,χ)| is of such a large order. More precisely, for every fixed σ∈(1/2,1), we show that for all sufficiently large q, there is a non-principal character χ(modq) such that log|L(σ,χ)|≥C(σ)(logq)1−σ(loglogq)−σ. In the case σ=1, we show that there is a non-principal character χ(modq) for which |L(1,χ)|≥eγ(log2q+log3q−C). In both cases, our results essentially match the prediction for the actual order of such extreme values, based on probabilistic models.

Menon-type identities concerning Dirichlet characters

Let [Formula: see text] be a Dirichlet character (mod [Formula: see text]) with conductor [Formula: see text]. In a quite recent paper Zhao and Cao deduced the identity [Formula: see text], which reduces to Menon’s identity if [Formula: see text] is the principal character (mod [Formula: see text]). We generalize the above identity by considering even functions (mod [Formula: see text]), and offer an alternative approach to prove. We also obtain certain related formulas concerning Ramanujan sums.

Snow White and the Seven Dwarfs, Cinderella and Sleeping Beauty: The Components of Costume Design in Disney’s Early Hand-Drawn Animated Feature Films

Costumes in feature films can be deliberately used for narrative purposes to reveal or conceal something related to the plot, functioning as a key element for cinematic storytelling. Costume design in animation is an integral part of character creation; however, relatively little is known about the design process. Previous research concentrates on either the history of hand-drawn animation, the principles of making animated films or character construction. This article presents several key components of the animators’ costume design process in Walt Disney’s animated feature films Snow White and the Seven Dwarfs (1937), Cinderella (1950) and Sleeping Beauty (1959). The author demonstrates that the costume design in these films was a multi-layered process. For example, for Snow White, the costume silhouette of the final animation is visible in the early conceptual designs whereas, for Cinderella or Princess Aurora, the principal character animators designed the final costume. Additionally, the slow production time influenced the style of the costumes: small details on costumes and complex constructions were not used as it would have taken too long for them to be drawn. The article also reveals that animators used live-action filming and rotoscoping as tools for designing costumes. Furthermore, costumes that were used in pre-production filming for rotoscope were different in their construction from everyday garments. The work of a costume designer existed in the character design process, although not as a separate profession. This article aims to highlight the importance of characters’ costumes in Disney’s early hand-drawn animated films and the different ways costumes have been designed for animated characters.