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A meromorphic function f(z)=z-1+a0+a1z+...is starlike of reciprocal order αif -Ref(z)/(zf′(z))>αfor all zin the unit disc. Using the theory of first order differential subordination an admissible condition is obtained so that Ψ(QST(z),QCV(z);z)∈Ωwhere QST(z)=-(zf′(z)/f(z))and QCV(z)=-(1+(zf′′(z))/f′(z))implies that fis starlike of reciprocal order α. Applying this result, various sufficient conditions are obtained for functions belonging to the class of all meromorphic starlike functions of reciprocal order α, for 0<α<1. Some sufficient conditions for functions fare obtained so that the image of f(z)/(zf′(z))lies inside the disc centered at -1with radius (1-α).

For 0⩽α<1, a normalised analytic function fdefined on the unit disc Dis convex of order αif ReQCV(f)>α, where QCV(f):=1+zf′′(z)/f′(z). We find numerous sufficient conditions for the function fto be a convex function of order αin terms of QCV(f)and QSD(f):=z2{f,z}, where {f,z}:=(f′′(z)/f′(z))′-(f′′(z)/f′(z))2/2is the Schwarzian derivative of f. We obtain these conditions by using the theory of second order differential subordination.

For a normalised analytic function fdefined on the open unit disk in the complex plane, we determine several sufficient conditions for starlikeness in terms of the quotients QST(z):=zf′(z)/f(z), QCV(z):=1+zf′′(z)/f′(z)and the Schwarzian derivative QSD(z):=z2(f′′(z)/f′(z)′-f′′(z)/f′(z)2/2). These conditions were obtained by using the admissibility criteria of starlikeness in the theory of second order differential subordination.

A normalized analytic function defined on the open unit disk is a bounded turning function if its derivative has positive real part. Such functions are univalent, and therefore, we find sufficient conditions for a function to be a bounded turning function. In this paper, we prove a general differential subordination theorem in terms of the derivative, the pre-Schwarzian derivative, and the Schwarzian derivative, providing sufficient conditions for a function to be a bounded turning function. We then apply the result to obtain several simple sufficient conditions.

A bi-univalent function is a univalent function defined on the unit disk for which the inverse function has a univalent extension to the unit disk. The paper of H. M. Srivastava, A. K. Mishra and P. Gochhayat [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), no. 10, 1188-1192] renewed the investigation of the estimate on initial coefficients of bi-univalent functions. In this paper, estimates for the initial coefficients of bi-univalent functions belonging to certain classes defined by subordination and of functions for which f and [f.sup.-1] belong to different subclasses of univalent functions are derived. Improvement of the earlier known estimates were also pointed out. Keywords and Phrases: Univalent functions, Bi-univalent functions, Coefficient estimate, Subordination., 1. Introduction Let A be the class of analytic functions defined on the open unit disk D: = {z [member of] C : [absolute value of z] < 1} and [...]

Numerous linear operators were introduced in geometric function theory and the properties of functions defined by them were derived using a recurrence relation satisfied by them. All these linear operators are unified in this paper and subordination and superordination properties of p-valent analytic functions defined using the general linear operator as well as a related integral transform are investigated. Some applications to univalent functions are also provided. Keywords and Phrases: p-valent function, Linear operator, Starlike function, Strongly starlike function., 1. Introduction Let H be the class of functions analytic in the unit disk D := {z ∈ C : [absolute value of z] < 1} and H[a, n] be [...]

The theory of second order differential subordination of S.S. Miller and P.T. Mocanu [Differential Subordinations, Dekker, New York, 2000] was recently extended to functions with fixed initial coefficient by R.M. Ali, S. Nagpal and V. Ravichandran [Second-order differential subordination for analytic functions with fixed initial coefficient, Bull. Malays. Math. Sci. Soc. (2) 34 (2011), 611-629] and applied to obtain several generalization of classical results in geometric function theory. In this paper, further applications of this subordination theory is given. In particular, several sufficient conditions related to starlikeness, convexity, close-to-convexity of normalized analytic functions are derived. Keywords and Phrases: Analytic functions, Starlike functions, Convex functions, Subordination, Fixed second coefficient., 1. Introduction For univalent functions f(z) = z + [[SIGMA].sub.n=2.sup.[infinity]] [a.sub.n] [z.sup.n] defined on D: {z [member of] C: |z| < 1}, the famous Bieberbach theorem shows that |[a.sub.2]| [less [...]

A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to be in certain subclasses of functions are established in terms of the Schwarzian derivatives and the second coefficients. These include obtaining a sufficient condition for functions to be strongly α-Bazilevic of order β. Keywords and Phrases: Univalent functions, Bazilevic functions, Gronwall's inequality, Schwarzian derivative, Second coefficient., 1. Introduction Let A be the set of all normalized analytic functions f of the form f(z) = z + [∑.sub.k=2.sup.∞][a.sub.k][z.sup.k] defined in the open unit disk D: = {z [...]

The function Gα(z)=1+z/(1-αz2),   0≤α<1, maps the open unit disk Donto the interior of a domain known as the Booth lemniscate. Associated with this function Gαis the recently introduced class BS(α)consisting of normalized analytic functions fon Dsatisfying the subordination zf′(z)/f(z)≺Gα(z). Of interest is its connection with known classes Mof functions in the sense g(z)=(1/r)f(rz)belongs to BS(α)for some rin (0, 1) and all f∈M. We find the largest radius rfor different classes M, particularly when Mis the class of starlike functions of order β, or the Janowski class of starlike functions. As a primary tool for this purpose, we find the radius of the largest disk contained in Gα(D)and centered at a certain point a∈R.

Some differential implications of classical Marx–Strohhäcker theorem are extended for multivalent functions. These results are also generalized for functions with fixed second coefficient by using the theory of first order differential subordination which in turn, corrects the results of Selvaraj and Stelin (Int J Math Anal 9(18): 883–895, 2015).

Let pbe an analytic function defined on the open unit disc Dwith p(0)=1and 0<α≤1. The conditions on complex valued functions C, D, and Eare obtained for pto be subordinate to ((1+z)/(1-z))αwhen C(z)z2p′′(z)+D(z)zp′(z)+E(z)p(z)=0. Sufficient conditions for confluent (Kummer) hypergeometric function and generalized and normalized Bessel function of the first kind of complex order to be subordinate to ((1+z)/(1-z))αare obtained as applications. The conditions on αand βare derived for pto be subordinate to ((1+z)/(1-z))αwhen 1+βzp′(z)/pn(z)with n=1,2is subordinate to 1+4z/3+2z2/3=:φCAR(z). Similar problems were investigated for Rep(z)>0when the function p(z)+βzp′(z)/pn(z)with n=0,2is subordinate to φCAR(z). The condition on βis determined for pto be subordinate to ((1+z)/(1-z))αwhen p(z)+βzp′(z)/pn(z)with n=0,1,2is subordinate to ((1+z)/(1-z))α.

Given two harmonic functions f1=h1+g¯1and f2=h2+g¯2defined on the open unit disk of the complex plane, the geometric properties of the product f1⊗f2defined by f1⊗f2=h1∗h2-g1∗g2¯+iIm(h1∗g2+h2∗g1)are discussed. Here ∗denotes the analytic convolution. Sufficient conditions are obtained for the product to be univalent and convex in the direction of the real axis. In addition, a convolution theorem, coefficient inequalities and closure properties for the product ⊗are proved.

We consider normalized analytic function fon the open unit disk for which either Ref(z)/g(z)>0, |f(z)/g(z)-1|<1or Re(1-z2)f(z)/z>0for some analytic function gwith Re(1-z2)g(z)/z>0. We have obtained the radii for these functions to belong to various subclasses of starlike functions. The subclasses considered include the classes of starlike functions of order α, lemniscate starlike functions and parabolic starlike functions.

A normalized analytic function fis lemniscate starlike if the quantity zf′(z)/f(z)lies in the region bounded by the right half of the lemniscate of Bernoulli |w2-1|=1. It is Janowski starlike if the quantity zf′(z)/f(z)lies in the disk whose diametric end points are (1-A)/(1-B)and (1+A)/(1+B)for -1≤B

For an analytic function fof the form f(z)=z+a2z2+a3z3+⋯satisfying either Re((f′(z))α(zf′(z)/f(z))(1-α))>0or Re((f′(z))α(1+zf′′(z)/f′(z))(1-α))>0, the bounds for the third Hankel determinant H3(1)=a3(a2a4-a32)-a4(a4-a2a3)+a5(a3-a22)are obtained. Our results include some previously known results.

For each a∈[0,1), the convolution of the right half-plane harmonic mapping having dilatation (a-z)/(1-az)with the right half-plane harmonic mapping having dilatation a-z2/1-az2or -(a-z)2/(1-az)2is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings fi=hi+gi¯, i=1,2satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,to be univalent and convex in the real direction.

We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

Let $${\mathcal {S}}^*_s$$Ss∗be the class of normalized analytic functions fdefined on the unit disk such that the quantity $$zf'(z)/f(z)$$zf′(z)/f(z)lies in an eight-shaped region in the right-half plane, which is the image of the unit disk under an entire function defined by $$\varphi (z)=1+\sin z$$φ(z)=1+sinz. For this class, we determine the $${\mathcal {S}}^*_s$$Ss∗-radii for the class of Janowski starlike functions and some other geometrically defined classes. A relation between this class and the class of Janowski starlike functions is also discussed.

Let fbe the function defined on the open unit disk, with $$f(0)=0=f'(0)-1$$f(0)=0=f′(0)-1, satisfying the subordinations $$zf'(z)/f(z)\prec \alpha + (1-\alpha )e^{z}$$zf′(z)/f(z)≺α+(1-α)ezor $$zf'(z)/f(z)\prec \alpha + (1-\alpha )\sqrt{1+ z}$$zf′(z)/f(z)≺α+(1-α)1+zrespectively, where $$0\le \alpha < 1$$0≤α<1. The sharp radii has been determined for these functions to belong to several well-known classes. In addition, some inclusion relations and coefficient estimates are also obtained.

The convolution properties are discussed for the complex-valued harmonic functions on the unit disk $$\mathbb {D}$$ D constructed from the harmonic shearing of the analytic function $$\phi (z):=\int _0^z (1-2\xi \textit{e}^{\textit{i}\mu }\cos \nu +\xi ^2\textit{e}^{2\textit{i}\mu })^{-1}{} \textit{d}\xi $$ ϕ(z):=∫0z(1-2ξeiμcosν+ξ2e2iμ)-1dξ , where $$\mu $$ μ and $$\nu $$ ν are real numbers. For any real number $$\alpha $$ α and a harmonic function $$f=h+\overline{g}$$ f=h+g¯ , define an analytic function $$f_{\alpha }$$ fα by $$f_{\alpha }:=h+\textit{e}^{-2\textit{i}\alpha }g$$ fα:=h+e-2iαg . Let $$\mu _1$$ μ1 and $$\mu _2$$ μ2 $$(\mu _1+\mu _2=\mu )$$ (μ1+μ2=μ) be real numbers, and $$f=h+\overline{g}$$ f=h+g¯ and $$F=H+\overline{G}$$ F=H+G¯ be locally univalent and sense-preserving harmonic functions such that $$f_{\mu _1}*F_{\mu _2}=\phi $$ fμ1∗Fμ2=ϕ . It is shown that the convolution $$f*F$$ f∗F is univalent and convex in the direction of $$-\,\mu $$ -μ , provided it is locally univalent and sense-preserving. Also, local univalence of the above convolution $$f*F$$ f∗F is shown when fand Fhave specific analytic dilatations. Furthermore, if $$g\equiv 0$$ g≡0 and both the analytic functions $$f_{\mu _1}$$ fμ1 and $$F_{\mu _2}$$ Fμ2 are convex, then the convolution $$f*F$$ f∗F is shown to be convex. These results extend the work of Dorff et al. (Complex Var Elliptic Equ 57(5):489–503, 2012) to a larger class of functions.

For three different normalizations of Bessel functions of first kind, the radius of k-parabolic starlikeness and k-uniform convexity of order $$\alpha $$ α are determined. The radius of strong starlikeness and other related radius are also obtained for these functions. We also find optimal parameters for which these functions are k-parabolic starlike and k-uniformly convex in the open unit disk.

Nitrogen (N) is a vital element for plant development and growth, and the application of N fertilizer could significantly increase yield formation in rice. One potential approach to reduce N fertilizer application in rice production is the development of varieties with improved nitrogen use efficiency. This study was investigating the genotypic differences of rice in the physiological nitrogen use efficiency and yield traits under different nitrogen levels. The photosynthetic rate was recorded higher (36.91 μmol CO2m−2s−1) in the treatment of 150% of recommmended nitrogen with rice genotype CB-08-513 at 50% flowering stage. The higher SPAD meter value (44.23) and leaf thickness (0.87 mm) were recorded in the recommended nitrogen with the genotype of CB-08-513. Regarding nitrogen content, the leaf nitrogen (5.43%) and total nitrogen content (1.86%) was recorded higher in medium duration genotypes under 150% of recommmended Nitrogen level at panicle initiation stage. The Nitrogen Uptake Efficiency (1.73), Physiological Nitrogen Use Efficiency (29.39), Nitrogen Utilization Efficiency (3.17), photosynthetic nitrogen use efficiency (4.74) were lower in medium duration genotypes when treated with 150% of recommmended Nitrogen. The maximum grain yield of 9160 kg ha−1was registered in medium duration genotype CO 50 under 150% of recommmended Nitrogen with increase of 20.62% over control. However, in short duration genotype CB-08-504 was recorded maximum grain yield of 8449 kg ha−1under 150% of recommmended Nitrogen with increase of 21.41% compared to 50% of recommmended Nitrogen.

Let $$-1 \le B

Ultra fine magnetic particles of NixFe100-xalloys were synthesized by a novel chemical reduction of the precursor salts by an alkali earth metal (Al) in an aqueous medium. In this method we successfully prepared alloy nanocrystalline powders without any bimetallic phases. The alloys were formed with Fe at% in two distinct bands 18–30 and 60–90 irrespective of the concentration ratios of Ni and Fe sources. The NixFe100-xalloy composition showed a transformation from fccto bccstructure .The Ni rich alloys namely NixFe100-x(x = 90 to75) which correspond to 18–30 band Fe at%.composition were formed in fcc (or simple cubic) phase, whereas the Fe rich alloys (x = 80) which correspond to 66–90 band Fe at%.composition were formed in bcc phase. The observed grain sizes for Ni rich (i.e., 18–30 Fe at.%) alloys lie in the range of 6–9 nm whereas for the Fe rich alloys grains are in the 20–27 nm range. Magnetization measurements shows that all the alloys exhibit ferromagnetic behaviour and the saturation magnetization values increase linearly with iron content. Vibrating sample magnetometer measurements shows that all samples exhibit ferromagnetic behaviour with increasing saturation magnetization as a function of iron content. SEM studies shows that the particles were found be large and agglomerated.

For a function fstarlike of order α, 0⩽α<1, a non-constant polynomial Qof degree nwhich is non-vanishing in the unit disc Dand β>0, we consider the function F:D→Cdefined by F(z)=f(z)(Q(z))β/nand find the largest value of r∈(0,1]such that r-1F(rz)lies in various known subclasses of starlike functions such as the class of starlike functions of order λ, the classes of starlike functions associated with the exponential function, cardioid, a rational function, nephroid domain and modified sigmoid function. Our radii results are sharp. We also discuss the correlation with known radii results as special cases.

Let $$\mathcal {S}^*_C$$ SC∗ be the class of normalized analytic functions fin the unit disc with $$zf'(z)/f(z)$$ zf′(z)/f(z) lying in the region bounded by the cardioid given by the equation $$(9 x^2+9 y^2-18x+5)^2- 16 (9 x^2+9 y^2-6x+1)=0$$ (9x2+9y2-18x+5)2-16(9x2+9y2-6x+1)=0 . We determine the structural formula, coefficient estimates, growth results and various radii constants such as the radius of starlikeness, radius of lemniscate of Bernoulli starlikeness, radius of M-starlikeness and radius of $$\mathcal {M}(\beta )$$ M(β) -starlikeness for functions in the class $$\mathcal {S}^*_C$$ SC∗ . In addition, the $$\mathcal {S}^*_C$$ SC∗ -radii for functions belonging to several interesting classes are determined. All the results obtained are sharp.

In this paper, we investigate the sufficient conditions for an analytic function fdefined in the open unit disk D⊆Csatisfying f(0)=f′(0)-1=0, such that the function fsatisfies zf′(z)f(z)2-1<2zf′(z)f(z),(z∈D).Let H(D)denote the class of analytic functions defined in Dand let H[1,n]:={pn∈H(D):pn(z)=1+anzn+an+1zn+1+...}, n∈N. We derive the admissibility conditions for the function q(z):=z+1+z2, which maps Dto the crescent-shaped region and use it to establish the result if the function pn∈H[1,n]with Repn(z)>2-1satisfies the second ordered differential condition |z2pn″(z)/pn(z)|<(n2(1+2)-2n)/22, (z∈D)then pn≺q. We also find several first order differential sufficient conditions for the function pnto obey the subordination pn≺q. Moreover, we provide examples to demonstrate the existence of the functions pn∈H[1,n]to satisfy these sufficient conditions.

Let $$\fancyscript{S}_{e}^*$$ Se∗ denote the class of analytic functions $$f$$ f in the open unit disk normalized by $$f(0)=f'(0)-1=0$$ f(0)=f′(0)-1=0 and satisfying the condition $$zf'(z)/f(z)\prec e^z$$ zf′(z)/f(z)≺ez for $$|z|<1$$ |z|<1 . The structural formula, inclusion relations, coefficient estimates, growth and distortion results, subordination theorems and various radii constants for functions in the class $$\fancyscript{S}_{e}^*$$ Se∗ are obtained. In addition, the sharp $$\fancyscript{S}_{e}^*$$ Se∗ -radii for functions belonging to several interesting classes are also determined.

For 0 ≤ α < 1, the sharp radii of starlikeness and convexity of order α for functions of the form f(z) = z + a 2 z 2 + a 3 z 3 + ... whose Taylor coefficients a n satisfy the conditions |a 2| = 2b, 0 ≤ b ≤ 1, and |a n| ≤ n, M or M/n (M > 0) for n ≥ 3 are obtained. Also a class of functions related to Carathéodory functions is considered.

Natural substances extracted from plants have recently been considered as potential sunscreen resources owing to high ultraviolet ray absorption and antioxidant activity. The decrease in the intensity of UV radiation reaching the skin through sunscreens may reduce the risk of sun-induced skin cancer. The present study attempts to develop sunscreen lotions, possessing broad spectrum of anti-UV radiation effectiveness with reduced concentration of chemical UV filters, from the extracts of bioactive products such as Curcuma longaL. (Zingiberaceae), Aloe vera(Liliaceae) and Alpinia galangaWilld. The effectiveness of the product was evaluated using Sun Protection Factor (SPF). Curcumin was selected as potential bioactive agents due to their phytochemical compositions possessing considerable content of polyphenolic compounds and Alpinia galangais used as key ingredient in various commercial sunscreen lotions as it has skin protectant action against UV rays and boosts the activity of conventional sunscreens. The sunscreen lotions were prepared using three different compositions F1, F2 and F3 and evaluated for their stability, safety and SPF. Results showed that the sunscreen lotions were non-mutagenic, non-irritant, stable and possess SPF for normal skin. The efficacy when tested with a standard was observed to be same as that of a marketed sunscreen with SPF 55 and SPF 20. From the present study, formulation F2 having curcumin extract was proved to be stable and effective with high SPF compared to F1 and F3.Natural substances extracted from plants have recently been considered as potential sunscreen resources owing to high ultraviolet ray absorption and antioxidant activity. The decrease in the intensity of UV radiation reaching the skin through sunscreens may reduce the risk of sun-induced skin cancer. The present study attempts to develop sunscreen lotions, possessing broad spectrum of anti-UV radiation effectiveness with reduced concentration of chemical UV filters, from the extracts of bioactive products such as Curcuma longaL. (Zingiberaceae), Aloe vera(Liliaceae) and Alpinia galangaWilld. The effectiveness of the product was evaluated using Sun Protection Factor (SPF). Curcumin was selected as potential bioactive agents due to their phytochemical compositions possessing considerable content of polyphenolic compounds and Alpinia galangais used as key ingredient in various commercial sunscreen lotions as it has skin protectant action against UV rays and boosts the activity of conventional sunscreens. The sunscreen lotions were prepared using three different compositions F1, F2 and F3 and evaluated for their stability, safety and SPF. Results showed that the sunscreen lotions were non-mutagenic, non-irritant, stable and possess SPF for normal skin. The efficacy when tested with a standard was observed to be same as that of a marketed sunscreen with SPF 55 and SPF 20. From the present study, formulation F2 having curcumin extract was proved to be stable and effective with high SPF compared to F1 and F3.

Abstract: In this paper, the bit error rate (BER) performance of eight user (10.7 Gb/s per user) Optical code division multiple access (OCDMA) system using fiber bragg grating (FBG) encoder/decoder (E/D) is analyzed with a) optical thresholding b)optimum fixed decision thresholding and c)balanced detection. The two critical issues with OCDMA system is multiple access interference (MAI) and signal interference beat noise (BN).To mitigate these effects various coding schemes and receiver structures were presented and compared with the resulting BER without increasing much of the receiver complexity. The effects of photodetector and receiver noises are not considered as these noises have no much effect on the receiver performance. The system model is presented and the results are given highlighting the difference in performance.

Abstract: Differential subordination and superordination results are obtained for analytic functions in the open unit disk which are associated with the Dziok–Srivastava linear operator. These results are obtained by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained. [ABSTRACT FROM AUTHOR]

Nanocrystalline Fe53Co47alloy was synthesized by a single‐step transmetallation chemical method at room temperature. The Fe53Co47alloy nanoparticles of 77 and 47 wt% were dispersed in silica matrix by the sol–gel process using tetraethyl orthosilcate. Structural studies reveal that the as‐prepared alloy powders are in bcc phase and silica is in an amorphous state. The phase‐transition temperature and Mössbauer spectra analysis of the Fe–Co alloy establishes the homogeneous alloy formation. A saturation magnetization of 218 emu/g was obtained for pure FeCo alloy at room temperature. Scanning electron microscopic analysis demonstrates the hollow‐sphere morphology for FeCo alloy particles. Magnetic nanocomposite consisting of 47 wt% FeCo–silica shows enhanced thermal stability over the native FeCo alloy. Electrical and dielectric properties of 47 wt% FeCo–silica nanocomposites were investigated as a function of frequency and temperature. It was found that the dielectric constants and dielectric loss were stable throughout the measured temperature (310–373 K). Our results indicate that FeCo–silica nanocomposite is a promising candidate for high‐frequency applications.

In this paper, the performance of coherence multiplexed(CM) turbo-coded optical PPM CDMA network is evaluated in terms of bit-error-rate (BER), number of users (K) and for various interleaver lengths (N) taking into account the effects of the thermal noise ad shot noise of APD detectors. For a fixed K(=10), the BER of a CM system is reduced by an order of 10−5than that of the single-ended direct detection system. For a typical data rate of 1Gb/s, and a specified BER of 10−6, it is found that the number of simultaneous users increases to 50. Turbo decoding is done using Log-MAP algorithm with different interleaver lengths of N=10, 50, 100 resulting in the reduction of BER to 10−9, 10−10and 10−11respectively and by applying performance bounds on the turbo-coded system, the maximum number of iterations to reach a BER of 10−14are limited to four in this system.

The combined effects of polarization mode dispersion (PMD) and polarization dependent loss (PDL) on pulse narrowing are considered for analysis. A multivariable search algorithm capable of finding optimum values of angle describing the input linear polarization, input frequency and PDL that influence pulse narrowing is presented and compared with single variable search algorithm. The multivariable search algorithm resulted in a pulsewidth reduction of 33.49% compared to 31.4% in single variable search algorithm, achieving a further reduction of 2.09%.

We obtain several results concerning the differential subordination between analytic functions and a linear operator defined for a certain family of analytic functions which are introduced here by means of these linear operators. Also, some special cases are considered.

New classes of codes, namely extended modified prime sequence codes (EMPSC) and difference codes, both having an ideal in-phase cross-correlation (IPCC) value of one, are suggested for spectral-amplitude-coding optical code-division multiple-access communication systems. The general structure of the system is discussed with simpler encoder and decoder architectures based on fiber Bragg gratings. Since the influence of multiuser interference can be completely removed due to ideal IPCC, the performance analyses of the proposed codes have been carried out by incorporating the effects of phase-induced intensity noise (PIIN), shot noise, and thermal noise at the receiver, employing Gaussian approximation. Assuming typical system parameters, evaluation results show that with an increase in code weight, the maximum number of accommodative users in the system can be increased as well as significant improvements in bit error probability for a given number of active users. For the same code weight, the difference codes can support a greater number of simultaneous users than the other. It is found that the effects of PIIN dominate compared to shot noise and thermal noise at large powers, whereas the effects of PIIN and shot noise are highly reduced at low powers, so that thermal noise becomes a more influential limitation factor. In comparison with earlier codes, the error performance of EMPSC is similar to that of modified quadratic congruence codes, while difference codes resemble those codes developed based on Steiner systems. © 2004 Society of Photo-Optical Instrumentation Engineers.

Bidirectional associative memories are used in pattern recognition applications and store the given input-output pairs. An important consideration in pattern association applications is the stability and recall accuracy of a given neural network. Some conditions for stability of library vectors using Hamming distances in a bidirectional associative memory are discussed. We also discuss the conditions for correct retrieval of stable states in a bidirectional associative memory. We derive the conditions for correct retrieval in terms of the maximum and minimum of the correlations as well as the number of pattern pairs and the size of the pattern vectors.

This paper discusses the generalized recursive structure for one-dimensional discrete cosine transform and discrete sine transform. This result in quicker computation of the discrete cosine and sine transform coefficients. The paper also looks at the relations among the family of discrete cosine and sine transforms and presents the mapping relationships for various discrete cosine and sine transforms. The results suggest that they can be utilized in various applications like data compression and VLSI implementations that utilize the quick discrete cosine transform and the quick discrete sine transform.

An analytic function f(z)=z+a n+1 z n+1+⋯ , defined on the unit disk △={z:|z|<1} , is in the class S p if z f′(z)/f(z) is in the parabolic region Rew>|w−1| . This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in S p are obtained. In particular, we find condition on λ such that the function f(z) , satisfying (1−α)(f(z)/z) μ+αf′(z)(f(z)/z) μ−1≺1+λz , is in S p .

The performance of multiwavelength optical orthogonal code-division multiple-access (MWOOCDMA) communication networks coupled into a single mode fiber (SMF) is evaluated at longer wavelengths (1300 - and 1550 - nm) with avalanche photodiode (APD) receiver in this paper. Analysis reveals that bit-error-rate (BER) probabilities are found to be minimum for M-ary signaling (M=8) and are 2.5377e-16 at 1300nm and 1.9032e-16 at 1550nm respectively compared to binary signaling (M=2) and are 1.6652e-9 at 1300nm 1.3242e-12 at 1550nm for optimum number of users, K=18 (max K=24) with received laser power, Ps=−45dBm, mean APD gain, G=100 with data rate, Rb= 1Gb/s.

In this paper, a theoretical investigation has been carried out to evaluate the performance of MWOOC’S using M-ary signaling in a OCDMA system employing multimode optical fiber. The performance is analysed in a multiuser interference (MUI) environment considering various noises such as modal noise in the optical fiber shot noise, APD bulk leakage noise, surface leakage noise, thermal noise in the receiver using the Gaussian approximation (GA) method. A two-dimensional (13×13,3,1,1) OOSPC using three wavelength (in the 825 nm range) that can support a maximum of 24 active users has been analysed for M=2,4 and 8 signals per user. The results suggest that M-ary signaling in the MWOOC’S is preferable to binary signaling for capacity enhancement of a OCDMA system.

Multiwavelength optical code-division multiple-access (CDMA) communication system employing 2nprime-sequence codes and extended prime codes are developed. Algorithms for the constructions of these codes are also given. Discrete number of wavelengths starting from 11 to 31 (prime numbers) are chosen for the analysis and the error performance curves are obtained as a function of number of simultaneous users of the system. Considering the effect of multiple users interference (MUI) alone and comparing the performance of these code families with that of generalised multiwavelength prime codes (GMWPC), better results are obtained in the former. It is also shown that an optical hard-limiter placed before the receiver correlator reduces error probability to a large extent.

The Protein Data Bank (PDB; http://www.rcsb.org/pdb/) is the single worldwide archive of structural data of biological macromolecules. This paper describes the data uniformity project that is underway to address the inconsistency in PDB data.