Convolutions of Harmonic Mappings Convex in the Horizontal Direction

In this paper, we establish some results concerning the convolutions of harmonic mappings convex in the horizontal direction with harmonic vertical strip mappings. Furthermore, we provide examples illustrated graphically with the help of Maple to illuminate the results.

Influence of Tillage Practices and Nitrogen Sources on Nitrogen Availability and Uptake of Rice

Aim: Evaluation of tillage practices and nitrogen sources on nitrogen availability in soil and nitrogen uptake of rice Study design: The experiment was laid out in strip-plot design with different tillage practices in horizontal strip and different nitrogen sources in vertical strip and was replicated thrice. Place and duration of study: The field experiment was conducted during the kharif season of 2019 and 2020 at the Agricultural College Farm, Bapatla, ANGRAU, Lam, Guntur, Andhra Pradesh. Methodology: The experiment was performed with twenty treatments in strip-plot design. The horizontal strip comprised four different tillage practices and vertical strip with five different nitrogen sources. Rice variety “BPT-5204” was taken as the test variety. Observations of the crop and soil during the experimentation were recorded at regular intervals. The significance of the treatment impact was examined by the test. Results: Among tillage practices, higher nitrogen uptake by rice grain (85.30 and 86.96 Kg ha-1) and straw (41.21 and 41.91 Kg ha-1) during 2019-20 and 2020-21, respectively was recorded in conventional tillage (T4) which was found statistically on a par with dry seeding on puddled soil (T1) (81.15 and 82.79 Kg ha-1, 38.59 and 39.20 Kg ha-1 during 2019-20 and 2020-21, respectively) and significantly superior over reduced tillage (T2) and minimum tillage (T3). Among nitrogen source, application of 50% STBN through fertilizer + 50% N through cured poultry manure (N5) registered the highest uptake of nitrogen in grain and straw (85.38 and 87.02 Kg ha-1. 42.09 and 42.76 Kg ha-1 during 2019-20 and 2020-21, respectively) and it was found significantly on a par with 75% STBN through fertilizer + 25% N through cured poultry manure (N4) and significantly superior over 50% STBN through fertilizer + 50% N through FYM (N3), 75% STBN through fertilizer + 25% N through FYM (N2), and 100% STBN through fertilizer (N1) treatment.

Numerical Modeling of Unreinforced Masonry Walls Strengthened with Fe-Based Shape Memory Alloy Strips

This study presents a new way to improve masonry wall behavior. Masonry structures comprise a significant part of the world’s structures. These structures are very vulnerable to earthquakes, and their performances need to be improved. One way to enhance the performances of such types of structures is the use of post-tensioning reinforcements. In the current study, the effects of shape memory alloy as post-tensioning reinforcements on originally unreinforced masonry walls were investigated using finite element simulations in Abaqus. The developed models were validated based on experimental results in the literature. Iron-based shape memory alloy strips were installed on masonry walls by three different configurations, namely in cross or vertical forms. Seven macroscopic masonry walls were modeled in Abaqus software and were subjected to cyclic loading protocol. Parameters such as stiffness, strength, durability, and energy dissipation of these models were then compared. According to the results, the Fe-based strips increased the strength, stiffness, and energy dissipation capacity. So that in the vertical-strip walls, the stiffness increases by 98.1%, and in the cross-strip model's position, the stiffness increases by 127.9%. In the vertical-strip model, the maximum resistance is equal to 108 kN, while in the end cycle, this number is reduced by almost half and reaches 40 kN, in the cross-strip model, the maximum resistance is equal to 104 kN, and in the final cycle, this number decreases by only 13.5% and reaches 90 kN. The scattering of Fe-based strips plays an important role in energy dissipation. Based on the observed behaviors, the greater the scattering, the higher the energy dissipation. The increase was more visible in the walls with the configuration of the crossed Fe-based strips.

A proof of a conjecture on convolution of harmonic mappings and some related problems

UDC 517.5 Recently, Kumar et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They have verified the above conjecture for and . Also, it has been proved only for . In this paper, by using of a new method, we settle this conjecture in the affirmative for all and . Moreover, we will use this method to prove some results on convolution of harmonic mappings. This new method simplifies calculations and shortens the proof of results remarkably.

Influence of Surroundings on Radiant Tube Lifetime in Indirect-Fired Vertical Strip Annealing Furnaces

The effects of surrounding radiation—emanating from radiation exchange with neighboring partners in indirect-fired vertical strip annealing furnaces, such as the other radiant tubes, the passing strip, and the enclosing furnace chamber—on the radiant tube lifetime were studied. In-house developed and validated numerical models were used to calculate the thermomechanical behavior, especially creep deformations and the corresponding stresses as lifetime indicating parameters. Different setups of recirculating P-type radiant tubes were investigated, including a reference case of an isolated tube. The investigations could be broadly classified into the study of the effects of different tube arrangements, burner operations (synchronous/asynchronous on/off firing), and changes of strip parameters (width/temperature). Results showed higher creep deformation of the central radiant tube in the setup with three tubes arranged horizontally in a row compared to three tubes stacked in a vertical column, even though the respective characteristic temperature values in a firing cycle were similar. Furthermore, the cases with asynchronous burner firing resulted in lower creep rates than other cases, where the burners were operating in synchronous on/off firing modes. In addition, the change of strip width had a higher impact on radiant tube lifetime compared to locally changing strip temperatures across the furnace. Alternating temperatures, caused by burner operation or process changes, such as change of strip’s speed or cross-section, and local temperature gradients were observed to be the main factors influencing the tube’s service life.

P-Partitions and p-Positivity

Using the combinatorics of $\alpha$-unimodal sets, we establish two new results in the theory of quasisymmetric functions. First, we obtain the expansion of the fundamental basis into quasisymmetric power sums. Secondly, we prove that generating functions of reverse $P$-partitions expand positively into quasisymmetric power sums. Consequently, any nonnegative linear combination of such functions is $p$-positive whenever it is symmetric. As an application, we derive positivity results for chromatic quasisymmetric functions, unicellular and vertical strip LLT polynomials, multivariate Tutte polynomials, and the more general $B$-polynomials, matroid quasisymmetric functions, and certain Eulerian quasisymmetric functions, thus reproving and improving on numerous results in the literature.

METHOD FOR ASSESSING SURFACE QUALITY OF COPPER CATHODES

In order to stabilize spiral elongation number at the required level (in accordance with the requirements of the European standard EN 12893 not less than 400 mm) the assessment of its distribution on the cathode sheet was carried out. The experimentally obtained results, processed using methods of mathematical statistics, showed significant discrepancies between the values of spiral elongation in the central and other parts of the cathode (upper, lower, side), which indicates an uneven distribution of the spiral elongation number along the cathode sheet. It was found that in order to form a representative analytical sample under cathode copper production of the Polar Division of MMC «Norilsk Nickel», the testing of cathodes should be performed using methods that include all areas of the cathode sheet, for example, cutting of a vertical strip from each cathode which has got in a representative sample, including edges and hanging ears. To determine the dependence of the spiral elongation number on the surface quality of copper cathodes, developed a special technique, based on the detection of the most frequently encountered defects in the surface of the cathode sheet, which assigned a certain numerical value in accordance with the ranking results. The proposed scoring system for the quality of cathodes in appearance allowed us to establish for the first time that stabilization of the spiral elongation number at a level of at least 400 mm is possible if the defectiveness of the cathode surface does not exceed 17 points per one electrolysis bath. The method has found practical application for preliminary quantitative estimation of the most widespread superficial defects of copper cathodes in the conditions of current production.

A Compact CPW-Fed Dual-Band Planar Monopole Antenna for LTE/2.4-GHz/WiMAX, C-Band and HiperLAN/2 Applications

In this paper, we present the design of a compact planar monopole antenna for dual-band wireless communication applications. The proposed antenna is based on a planar structure composed by a CPW feed line and a rectangular ring with a vertical strip. The designed antenna has a small overall size of [Formula: see text][Formula: see text]mm3. Dual-band characteristics can be obtained by adjusting the distance between the rectangular ring and the ground plane of the CPW feed line, as well as the dimensions of the rectangular ring and the length of the vertical strip. A prototype of the proposed antenna which was fabricated and measured to validate the design reveals that there is a good agreement between the simulation and the experiment. The measured result shows that the antenna has the impedance bandwidths of 610[Formula: see text]MHz (2–2.61[Formula: see text]GHz) and 2600[Formula: see text]MHz (3.18–5.78[Formula: see text]GHz) with a reflection coefficient less than [Formula: see text]10[Formula: see text]dB covering all the LTE 2300, 2.4-GHz band, WiMAX, C-band and HiperLAN/2 applications. In addition, the dual-band monopole antenna exhibits almost omnidirectional radiation patterns and an appreciable gain over the operating frequency bands. Details of the proposed antenna design and both simulated and experimental results are analyzed and discussed.