Zeros of a Function

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Distribution of zeros of discrete and continuous polynomials from their recurrence relation.

Distribution of zeros of discrete and continuous polynomials from their recurrence relation.

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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E. Buend a - The distribution of zeros of general q-polynomials.

E. Buend a - The distribution of zeros of general q-polynomials.

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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On weighted average interpolation with cardinal splines

On weighted average interpolation with cardinal splines

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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INTERPOLATION OF LOW-ORDER HRTF FILTERS USING A ZERO DISPLACEMENT MEASURE

INTERPOLATION OF LOW-ORDER HRTF FILTERS USING A ZERO DISPLACEMENT MEASURE

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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Variations of the Similarity Function of TextRank for Automated Summarization

Variations of the Similarity Function of TextRank for Automated Summarization

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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TítuloOptimal Synthesis of Line Source Antennas Based On Rhodes Distributions

TítuloOptimal Synthesis of Line Source Antennas Based On Rhodes Distributions

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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Another proof of characterization of BMO via Banach function spaces

Another proof of characterization of BMO via Banach function spaces

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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Properties of the bivariate confluent hypergeometric
            function kind 1 distribution

Properties of the bivariate confluent hypergeometric function kind 1 distribution

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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2016 Ardila Is self-conciousness equivalent to executive function

2016 Ardila Is self-conciousness equivalent to executive function

“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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Mitochondria and endocrine function of adipose tissue

Mitochondria and endocrine function of adipose tissue

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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Optical spatial soliton propagation through optical lattices with elliptic and circular symmetries

Optical spatial soliton propagation through optical lattices with elliptic and circular symmetries

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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TítuloPerturbation of the phases of Taylor field samples in the synthesis of linear and circular array antennas

TítuloPerturbation of the phases of Taylor field samples in the synthesis of linear and circular array antennas

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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GEOGRAPHIC INFORMATION SYSTEM FOR EVALUATION OF ROAD TRAFFIC NOISE ALONG THE ROAD

GEOGRAPHIC INFORMATION SYSTEM FOR EVALUATION OF ROAD TRAFFIC NOISE ALONG THE ROAD

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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Olfaction and the function of the paranasal sinuses

Olfaction and the function of the paranasal sinuses

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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Values of the Riemann zeta function
at integers.

Values of the Riemann zeta function at integers.

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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Zeta function regularization of holographic Wilson loops

Zeta function regularization of holographic Wilson loops

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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Normalizing or not normalizing? An open question for floating-point arithmetic in embedded systems

Normalizing or not normalizing? An open question for floating-point arithmetic in embedded systems

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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A generalization of the classical Laguerre polynomials: Asymptotic Properties and Zeros.

A generalization of the classical Laguerre polynomials: Asymptotic Properties and Zeros.

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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On the “Favard theorem” and its extensions

On the “Favard theorem” and its extensions

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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Assessment of different components of executive function in grief

Assessment of different components of executive function in grief

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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