On the Weyl’s Lemma for Triharmonic Functions

In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.

A Subclass of Harmonic Functions Associated with Wright’s Hypergeometric Functions

We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

THE SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS

In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.

A New Class of Harmonic Univalent Functions by the Generalized Salagean Operator

A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.

A New Class of Harmonic Univalent Functions

A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g,where h and g are analytic in U.We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions.We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β).These conditions are also shown to be necessary when the coefficients are negative.This leads to distortion bounds and extreme points.

Abnormal transition of the electron energy distribution with excitation of the second harmonic in low-pressure radio-frequency capacitively coupled plasmas

The self-excited second harmonic in radio-frequency capacitively coupled plasma was significantly enhanced by adjusting the external variable capacitor.At a lower pressure of 3 Pa,the excitation of the second harmonic caused an abnormal transition of the electron energy probability function,resulting in abrupt changes in the electron density and temperature.Such changes in the electron energy probability function as well as the electron density and temperature were not observed at the higher pressure of 16 Pa under similar harmonic changes.The phenomena are related to the influence of the second harmonic on stochastic heating,which is determined by both amplitude and the relative phase of the harmonics.The results suggest that the self-excited high-order harmonics must be considered in practical applications of lowpressure radio-frequency capacitively coupled plasmas.

High-Order Radial Derivatives of Harmonic Function and Gravity Anomaly

The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.

Several Hermite-Hadamard Type Inequalities for Harmonically Convex Functions in the Second Sense with Applications

In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.

Modeling, Steady-State Analysis of a SEPIC dc-dc Converter Based on Switching Function and Harmonic Balance Technique

The paper presents modeling approach of a Single Ended Primary Inductance Converter (SEPIC) system. The complete model derivation of the SEPIC converter system has been presented in different modes of operation. Steady state and small signal analysis was carried out on the converter dynamic equations using the method of Harmonic balance Technique. The steady state variables and their respective ripple quantities obtained were plotted against duty ratio D. The results obtained for a supply input voltage of 60 volts to the converter at a duty ratio of D = 0.8 , compares well with simulation results.

Investigation on the relationship between overpressure and sub-harmonic response from encapsulated microbubbles

Sub-harmonic component generated from microbubbles is proven to be potentially used in noninvasive blood pressure measurement. Both theoretical and experimental studies are performed in the present work to investigate the dependence of the sub-harmonic generation on the overpressure with different excitation pressure amplitudes and pulse lengths. With 4-MHz ultrasound excitation at an applied acoustic pressure amplitude of 0.24 MPa, the measured sub-harmonic amplitude exhibits a decreasing change as overpressure increases; while non-monotonic change is observed for the applied acoustic pressures of 0.36 MPa and 0.48 MPa, and the peak position in the curve of the sub-harmonic response versus the overpres- sure shifts toward higher overpressure as the excitation pressure amplitude increases. Furthermore, the exciting pulse with long duration could lead to a better sensitivity of the sub-harmonic response to overpressure. The measured results are ex- plained by the numerical simulations based on the Marmottant model. The numerical simulations qualitatively accord with the measured results. This work might provide a preliminary proof for the optimization of the noninvasive blood pressure measurement through using sub-harmonic generation from microbubbles.

Generalized Harmonic Numbers Hn,k,r (α,β) with Combinatorial Sequences

In this paper, we observe the generalized Harmonic numbers Hn,k,r (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers Hn,k,r (α,β) with Changhee sequences, Daehee sequences, Degenerate Changhee-Genoocchi sequences, Two kinds of degenerate Stirling numbers. Using Riordan arrays, we explore interesting relations between these polynomials, Apostol Bernoulli sequences, Apostol Euler sequences, Apostol Genoocchi sequences.

A Broadband 630-720 GHz Schottky Based Sub-Harmonic Mixer Using Intrinsic Resonances of Hammer-Head Filter

An room temperature low noise anti-parallel Schottky diode based 630-720 GHz sub-harmonic mixer(SHM) is designed, built and measured. Intrinsic resonances in lowpass hammer-head filter have been adopted to prevent the LO and RF power leak from the IF channel, while greatly minimizing the transmission line size. The mixer consists of 15 um quartz terahertz circuit and 127 um Al2 O3 IF transformer circuit. An improved lumped element equivalent noise model of SBDs guarantees the accuracy of simulation. The measurement indicates that with local oscillating(LO)signal of 2-8 mW, the lowest double sideband(DSB) conversion loss is 8.2 dB at 645 GHz,and the best DSB noise temperature is 2800 K at 657 GHz. The 3 dB bandwidth of conversion loss is 75 GHz from 638 to 715 GHz. The work IF frequency band is above 20 GHz ranging from 1 to 20 GHz with-10 dB return loss.

GRADIENT ESTIMATES FOR POSITIVE SMOOTH f-HARMONIC FUNCTIONS

For Riemannian manifolds with a measure, we study the gradient estimates for positive smooth f-harmonic functions when the ∞-Bakry-Emery Ricci tensor and Ricci tensor are bounded from below, generalizing the classical ones of Yau （i.e., when ： is constant）.

ON THE DIMENSIONS OF SPACES OF HARMONIC FUNCTIONS WITH POLYNOMIAL GROWTH

In this paper, we obtain an estimate for the lower bound for the dimensions of harmonic functions with polynomial growth and a Liouville type theorem on manifolds with nonnegative Ricci curvature whose tangent cone at infinity is a unique metric cone with a conic measure.

A SCHWARZ LEMMA FOR HARMONIC FUNCTIONS IN THE REAL UNIT BALL

We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.

CONSTRUCTION SPACE HARMONIC FUNCTIONS IN POLYN0MIAL FORM AND SPHERICAL FUNCTIONS BY COMPLEX-FUNCTIONAL

In this paper, applying the theory of complex-functional, not only the spaceharmonic functions in polynomial form. but aIso the spherical functions are obtained.

NUMERICAL COMPARISON OF TWO BOUNDARY ELEMENT METHODS FOR PLANE HARMONIC FUNCTIONS

A direct boundary element method (BEM) has been studied in the paper based on a set of sufficient and necessary boundary integral equations (BIE) for the plane harmonic functions. The new sufficient and necessary BEM leads to accurate results while the conventional insufficient BEM will lead to inaccurate results when the conventional BIE has multiple solutions. Theoretical and numerical analyses show that it is beneficial to use the sufficient and necessary BEM, to avoid hidden dangers due to non-unique solution of the conventional BIE.

Investigation of analytical harmonic frequency and potential energy function, vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.