Certain Classes of Analytic Functions Bound with Kober Operators in q -Calculus

Through applying the Kober fractional q -calculus apprehension, we preliminary implant and introduce new types of univalent analytical functions with a q -differintegral operator in the open disk U = ξ ∈ ℂ : ∣ ξ | < 1 . The coefficient inequality and distortion theorems are among the results examined with these forms of functions. Specific cases are responded and addressed immediately. The findings include an expansion of the numerous established results in the q -theory of analytical functions.

Thrust Force Measurements in an Axial Steam Turbine Test Rig: Effect of Disk Balance Holes

A full-size, full-speed, axial flow steam turbine test rig capable of measuring turbine thrust, and static pressures in the rotor-stator disk cavity was built and commissioned. The test rig was operated in a single-stage configuration for the test results first reported in Stasenko et al. [1], and now in this paper. The stage has stationary axial face seals radially inward of the airfoils, near the rotor disk rim. The face seals divide the rotor-stator cavity into inner and outer circumferential cavities, both of which were instrumented with static pressure probes on the stator radial wall. Axial thrust was measured with load cells in every thrust bearing pad. The test rig was operated over a range of three nominal stage pressure ratios (designated as LPR, MPR, and HPR), five nominal stage velocity ratios (0.25–0.6), and five admission fractions (0.38–0.88). This latest group of tests was conducted without rotor disk balance holes, which were mechanically plugged, and will be compared to the original block of tests with disk balance holes opened. In the upstream disk cavity, the two disk balance hole configurations shared many similar pressure characteristics: nearly uniform pressures in the inner cavity, circumferential pressure distributions in the outer cavity that corresponded with the direction of axial thrust, and radial pressure distributions in the outer cavity that were a direct function of rotor speed. General trends of thrust coefficients with the disk holes plugged were correlated to stage pressure ratio, stage velocity ratio, admission fraction, and leakage mass flow rate. Those trends were consistent with the first block of tests with open disk balance holes, although there was an offset toward more operating conditions with negative aggregate thrust coefficients. This suggests that the rotating disk induces a low-pressure gradient in the inner (upstream) cavity, and the opened disk balance holes tend to equalize the inner cavity static pressure toward the higher static pressure on the exit side of the disk. Additionally, thrust coefficients tended to become less negative (or more positive) with stage pressure ratio and with velocity ratio, but tended to become more negative with admission fraction. Significant thrust coefficient reductions were realized with the open disk balance hole configuration, and were determined to be consistently speed-dependent.

Univalence criteria for a general integral operator

"The main object of this paper is to give sufficient conditions for the general integral operator Tn, to be univalent in the open disk U, when gi, hi, ki ∈ Gbi for all i = 1, n. This general integral operator was considered in a recent work [Barbatu, C. and Breaz, D., ˘ Classes of an univalent integral operator, Studia Univ. Babes¸-Bolyai Math., accepted]. The results derived in this paper are shown to follow upon specializing the parameters involved in our results. Several corollaries of the main results are also considered."

Deformation limit and bimeromorphic embedding of Moishezon manifolds

Let [Formula: see text] be a holomorphic family of compact complex manifolds over an open disk in [Formula: see text]. If the fiber [Formula: see text] for each nonzero [Formula: see text] in an uncountable subset [Formula: see text] of [Formula: see text] is Moishezon and the reference fiber [Formula: see text] satisfies the local deformation invariance for Hodge number of type [Formula: see text] or admits a strongly Gauduchon metric introduced by D. Popovici, then [Formula: see text] is still Moishezon. We also obtain a bimeromorphic embedding [Formula: see text]. Our proof can be regarded as a new, algebraic proof of several results in this direction proposed and proved by Popovici in 2009, 2010 and 2013. However, our assumption with [Formula: see text] not necessarily being a limit point of [Formula: see text] and the bimeromorphic embedding are new. Our strategy of proof lies in constructing a global holomorphic line bundle over the total space of the holomorphic family and studying the bimeromorphic geometry of [Formula: see text]. S.-T. Yau’s solutions to certain degenerate Monge–Ampère equations are used.

Bounds of coefficients for classes of analytic functions related to hypergeometric functions

The main purpose of the present paper is to give some sharp coefficients bounds for a certain class of univalent analytic functions in unit open disk, which was defined by using principle of differential subordination and generalized hypergeometric function. As applications, we investigate the almost starlike-type functions, parabolic starlike-type functions and uniformly convex-type functions with conic domain. Our results extend some earlier works related to Ma-Minda starlike and convex functions.

On the convergence of multidimensional S-fractions with independent variables

In this paper, we investigate the convergence of multidimensional S-fractions with independent variables, which are a multidimensional generalization of S-fractions. These branched continued fractions are an efficient tool for the approximation of multivariable functions, which are represented by formal multiple power series. For establishing the convergence criteria, we use the convergence continuation theorem to extend the convergence, already known for a small region, to a larger region. As a result, we have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional S-fraction with independent variables. And, also, we have shown that the interior of the parabola is the domain of convergence of a branched continued fraction, which is reciprocal to the multidimensional S-fraction with independent variables. In addition, we have obtained two new convergence criteria for S-fractions as a consequences from the above mentioned results.