The global behaviour **of** the **zeros** **of** the discrete and continuous classical orthogonal poly- nomials in both nite and asymptotic cases has received a great deal **of** attention from the early times [22, 27, 45] **of** approximation theory up to now [8, 9, 20, 23, 24, 31, 32, 33, 34, 36, 37, 41, 42, 46, 47, 48, 50]. Indeed, numerous interesting results have been found from the dif- ferent characterizations (explicit expression, weight **function**, recurrence relation, second order dierence or dierential equation) **of** the polynomial. See [16] for a survey **of** the published results up to 1977; more recent discoveries are collected in [49] and [31] for continuos and dis- crete polynomials, respectively. Still now, however, there are open problems which are very relevant by their own and because **of** its numerous applications to a great variety **of** classical systems [29, 35] as well as quantum-mechanical systems whose wavefunctions are governed by orthogonal polynomials in a \discrete" [2, 3, 40, 43, 44] or a \continuous" variable [5, 18, 19, 39]. In this paper the attention will be addressed to the problem **of** determination **of** the moments **of** the distribution density **of** **zeros** for a classical orthogonal polynomial **of** a given order n in both discrete and continuous cases as well as its asymptotic values (i.e, when n ! 1 ), which

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The method **of** proof used is very straightforward. It is based on an explicit formula for the moments-around-the-origin **of** the discrete density **of** **zeros** **of** a polynomial with a given degree in terms **of** the coecients **of** the three term recurrence relation [37], as described in Lemma 1 given below. This method was previously employed to normal (non-q) polynomials where recurrence coecients are given by means **of** a rational **function** **of** the degree [38], as well as to correspond- ing Jacobi matrices [39] encountered in quantum mechanical description **of** some physical systems. The paper is structured as follows. Firstly, in section 2, one introduces a general set **of** q- polynomials f P n ( x ) q g Nn

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After this paper was flnished, the authors knew that the same result had been obtained independently and at the same time by Ponnaian and Shanmugam in [8]. Although both papers use Theorem 3, the way those authors follow to study the **zeros** **of** the G **function** is different from ours. Ponnaian and Shanmugam base their arguments on the study that they carry out about the roots **of** the exponential Euler splines. In particular, they need to obtain a recursion relation for those exponential splines. Moreover, they consider four different cases on the degree d. On the contrary, our arguments may be more direct, since we apply already known properties **of** the Euler-Frobenius polynomials and only have to consider even and odd degree cases separately.

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Head-related transfer **function** (HRTF) defines the spectral shaping **of** the sound signal on its way from a source location in the free field to the external ear. HRTFs are generally measured at discrete positions on a spherical grid equidistant from centre **of** the human head (or mannequin) whose measurements are being taken [1]. These measurements provide a set **of** HRTFs at discrete values **of** azimuth and elevation. The HRTFs provide a frequency dependent **function** **of** interaural intensity difference (IID) and a constant interaural time delay (ITD). The HRTF data obtained from these measurements are used for designing low-order digital filters to be made available for use in real-time audio spatialisation applications. A number **of** different approaches regarding the HRTF filter design process have been proposed [2][3][4].

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The selected text fragments to use in the graph construction can be phrases [6], sentences [14], or paragraphs [18]. Currently, many successful systems adopt the sentences considering the tradeoff between content richness and grammar correctness. According to these approach the most important sentences are the most connected ones in the graph and are used for building a final summary [2]. To identify relations between sentences (edges for the graph) there are sev- eral measures: overlapping words, cosine distance and query-sensitive similarity. Also, some authors have proposed combinations **of** the previous with supervised learning functions [19].

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Compared with the Taylor distribution for the same values **of** A and n , the Rhodes sum pattern has a slightly broader main beam; allows the use **of** larger values **of** n without incurring in superdirectivity; and, for u > n , has a slightly steeper side lobe taper. The amplitude **of** the Rhodes aperture distribution goes to zero linearly at the ends **of** the antenna, but the slope is steep and preceded by a sharp rise, so that the edge-brightening problem **of** Taylor distributions is not significantly ameliorated.

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R n ) with constant exponent 1 ≤ p ≤ ∞ is an example **of** Banach **function** spaces. Kov´ aˇ cik and R´ akosn´ık [12] have proved that the generalized Lebesgue space L p(·) ( R n ) with variable exponent p(·) is a Banach **function** space and the associate space is L p 0 (·) (

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In the next theorem we derive the bivariate confluent hypergeometric **function** kind 1 distribution using independent beta and gamma variables. First, we define beta type 1 and beta type 2 distributions. These definitions can be found in Johnson, Kotz and Balakrishnan [7].

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“Consciousness” is a complex concept that is not easily defined. The term consciousness is derived from the Latin word conscientia: con (with) and scire (to know). Etymologi- cally, consciousness means “to have knowl- edge.” Currently, different definitions **of** consciousness can be found. For example, the Merriam-Webster Dictionary (n.d.) de- fines consciousness as “the quality or state **of** being aware especially **of** something within oneself.” In his book, Psychology **of** Con- sciousness, Farthing (1992) included in the definition **of** consciousness the following: sentience, awareness, subjectivity, the ability to experience or to feel, wakefulness, having a sense **of** selfhood, and the executive control system **of** the mind. Notably, both “aware- ness” and “the executive control system **of** the mind” (i.e., metacognition) are included in this definition **of** consciousness. The Stanford

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7 Lee mas

Excess **of** adipose tissue is accompanied by an increase in the risk **of** developing insulin resistance, type 2 diabetes (T2D) and other complications. Nevertheless, total or partial absence **of** fat or its accumulation in other tissues (lipotoxicity) is also associated to these complications. White adipose tissue (WAT) was traditionally considered a metabolically active storage tissue for lipids while brown adipose tissue (BAT) was considered as a thermogenic adipose tissue with higher oxidative capacity. Nowadays, WAT is also considered an endocrine organ that contributes to energy homeostasis. Experimental evidence tends to link the malfunction **of** adipose mitochondria with the development **of** obesity and T2D. This review discusses the importance **of** mitochondrial **function** in adipocyte biology and the increased evidences **of** mitochondria dysfunction in these epidemics. New strategies targeting adipocyte mitochondria from WAT and BAT are also discussed as therapies against obesity and its complications in next future.

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In the later, oscillons are the result from vertically vibrating a plate with a layer **of** uniform particles placed freely on top. When the sinusoidal vibrations are **of** the correct amplitude and frequency and the layer **of** sufficient thickness, a localized wave, referred to as an oscillon, can be formed by locally disturbing the particles. This meta-stable state will remain for a long time (many hundreds **of** thousands **of** oscillations) in the absence **of** further perturba- tion. An oscillon changes form with each collision **of** the grain layer and the plate, switching between a peak that projects above the grain layer to a crater like depression with a small rim [8]. Whereas solitons are traveling waves, oscillons can be stationary. Oscillons have been experimentally observed in thin vibrating layers **of** viscous fluid and colloidal suspensions. Oscillons have been recently associated with Faraday waves because they require similar res- onance conditions. Nonlinear electrostatic oscillations on a plasma boundary can also appear in the form **of** oscillons.

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We considered the synthesis **of** a linear array with 19 elements a distance 0.7 apart that is required to generate a 20 dB Chebyshev-like pattern and to have an aperture distribution that lacks marked edge-brightening and is generally as smooth as possible in both amplitude and phase. These requirements were imposed by using the cost **function**

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In Japan, about one hundred and ten million people reside in a narrow country and there are a lot **of** residential buildings located along arterial roads. These buildings are fiercely affected by road traffic noise and prompt measures to noise should be taken. To deal with such a situation, the Ministry **of** Environment revised "Environmental Quality Standards for Noise" [1] and enforced it in April 1999. As a result, noise shall be evaluated by the equivalent continuous A-weighted sound pressure level (L Aeq ), and especially for areas facing roads, achievement shall in principle

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Obviously olfaction must play an important role, since while grazing it is difficult to keep a constant look out, and the high grass usually obstructs much **of** the view. Fortunately for the zebras, a lion being a carnivore, is not the cleanest **of** animals, and can often be smelled a proverbial mile off even with our rudimentary sense **of** smell. In fact all the zebras in the herd will have smelled the lions the whole time they were grazing near them, and yet they continued unconcerned and until one **of** the lions made a consistent move in their direction.

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to mention that before the computer era began roughly in the middle **of** the twentieth century, only about a thousand **zeros** were calculated. **Of** course all **of** these **zeros** are calculated with some (high) accuracy: they are lying on the critical line. However, there is no proof that really all nontrivial **zeros** lie on this line and this conjecture is called the Riemann Hypothesis.

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Our manuscript is a push in understanding the role **of** technical methods needed to tackle precision computations in holography and we are certain that its application will go beyond the one presented here. We hope to return, e.g., to a similar computation in the context **of** the Aharony- Bergman-Jafferis-Maldacena duality. It is also plausible that the methods systematically developed in our companion paper [12] and used explicitly here, will find use in other problems possibly related to one-loop super- gravity computations in the context **of** corrections to the black hole entropy.

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We also test intermediate solutions, where left-shifting is performed but only for a few bits. Fig. 2 shows this new adder that we denote as A2 (A2H for HUB version). Comparing it with A1, the A2 design has a special leading zero detector, which detects up to two leading **zeros** at the output **of** the absolute value circuit. Furthermore, it has a barrel shifter that can perform a one-position right-shifting (in case **of** detecting overflow) and left-shifting up to 2-bit positions. This will increase the area and the delay **of** the critical path, but it will improve the error figures as we will see in section V. In this architecture the exponent has to be decremented when left- shifting is performed, and therefore underflow could happen. Although it is not depicted in Fig. 2, this situation is detected in the design and the result flushes to zero.

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In 1940, H. L. Krall [14] obtained three new classes **of** polynomials orthogonal with respect to measures which are not absolutely continuous with respect to the Lebesgue measure. In fact, his study is related to an extension **of** the very well known characterization **of** classical orthogonal polynomials by S. Bochner. This kind **of** measures was not considered in [22].

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that the main dierence with the recurrence relation analyzed in Section 2 is that here only two consecutive polynomials are involved and the reciprocal polynomial is needed. On the other hand, the basic parameters which appear in these recurrence relations are the value at zero **of** the orthogonal polynomial.

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One possible explanation **of** their emotional decision-making performance is that a participant experiencing intense grief also experiences a dysregulation **of** the reward system that is generalized rather than specifi c to the death or biographical stimulus. This is in line with previous studies that point to an unpleasant emotional experience in participants with CG when they are exposed to positive and negative stimuli (Fernández-Alcántara et al., 2016). In addition, specifi c symptoms **of** CG, such as emotional numbness, may impede the adequate interpretation **of** current body signals during the IGT, with the consequence **of** insensitivity to punishment (e.g., a preference for decks A and B despite the consistent loss **of** an important amount **of** money) during the task. In addition, previous research has reported obstacles for future reward processing in participants with CG (Maccallum & Bonanno, 2015).

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