Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

A quantum circuit design of AES requiring fewer quantum qubits and gate operations

Advanced Encryption Standard (AES) is one of the most widely used block ciphers nowadays, and has been established as an encryption standard in 2001. Here we design AES-128 and the sample-AES (S-AES) quantum circuits for deciphering. In the quantum circuit of AES-128, we perform an affine transformation for the SubBytes part to solve the problem that the initial state of the output qubits in SubBytes is not the |0>^⊗8 state. After that, we are able to encode the new round sub-key on the qubits encoding the previous round sub-key, and this improvement reduces the number of qubits used by 224 compared with Langenberg et al.’s implementation. For S-AES, a complete quantum circuit is presented with only 48 qubits, which is already within the reach of existing noisy intermediate-scale quantum computers.     

Kinetics of carbon steel dissolution in ammonium chloride solution containing sodium thiosulfate

The dissolution behavior of carbon steel in ammonium chloride (NH₄Cl) solution containing sodium thiosulfate (Na₂S₂O₃) of various concentrations (0.01 and 0.1 M) was investigated using electrochemical impedance spectroscopy (EIS) and other nonelectrochemical techniques. The weight loss and polarization measurements indicate a significant increase in the NH₄Cl corrosion rate of carbon steel on addition of Na₂S₂O_3. The EIS measurements exhibited two capacitive loops at multiple direct current (dc) potentials for both the concentrations. Electrical equivalent circuit (EEC) and reaction mechanism analysis (RMA) were employed to analyze the impedance data. A four-step mechanism with two intermediate adsorbate species of same charge was proposed to explain the dissolution behavior of carbon steel in the given system. The surface coverage values enumerated that the surface was entirely covered with adsorbed species unlike in the pure NH₄Cl system. Charge transfer resistance and polarization resistance values estimated from RMA parameters indicate the increase in a dissolution rate with dc potential. The surface morphology was inspected via field emission scanning electron microscopy, and the corrosion products including surface state of carbon steel electrode were analyzed using energy dispersive X-ray spectroscopy and X-ray photoelectron spectroscopy.     

Printed Circuit Board-Based Electrolyte Regulator for Laminar Microfluidics

The trench on a printed circuit board was reconstructed to fabricate a microfluidic framework that allows low-cost production for small quantities and integration with multifunctional elements. An on-chip electrolyte regulator was thus proposed on this platform to analyze diffusion properties in laminar flow. A numerical model was developed, highlighting the interplay between the electrolyte migration and hydrodynamic properties. Solutions with dissolved sodium chloride were simulated and experimentally tested for the regulation of electrical conductivity under the guidance of the normalized Nernst-Planck equation. The diffusion mechanism and the resulting concentration field were demonstrated in detail. This approach provides a satisfactory manufacturing method and a useful tool for integrated microfluidic systems.     

A survey on HHL algorithm: From theory to application in quantum machine learning

The Harrow-Hassidim-Lloyd (HHL) algorithm is a method to solve the quantum linear system of equations that may be found at the core of various scientific applications and quantum machine learning models including the linear regression, support vector machines and recommender systems etc. After reviewing the necessary background on elementary quantum algorithms, we provide detailed account of how HHL is exploited in different quantum machine learning (QML) models, and how it provides the desired quantum speedup in all these models. At the end, we briefly discuss some of the remaining challenges ahead for HHL-based QML models and related methods.     

对史密斯-帕塞尔自由电子激光光栅的研究

为了研究史密斯-帕塞尔自由电子激光的输出频率和光栅槽深、光栅槽长、光栅槽宽的关系,对于基于矩形光栅的史密斯-帕塞尔自由电子激光利用粒子模拟软件进行模拟和理论分析。首先,利用粒子模拟软件模拟对于基于矩形光栅的史密斯-帕塞尔自由电子激光进行了研究,发现史密斯-帕塞尔自由电子激光的输出频率随光栅槽深、光栅槽长、光栅槽宽的增大而减少。接着,对史密斯-帕塞尔自由电子激光的光栅槽进行了理论分析,发现每个光栅槽都可以等效为一个LC谐振电路,并发现在史密斯-帕塞尔自由电子激光中存在两种辐射,一种是史密斯-帕塞尔辐射,另一种是LC振荡辐射。最后,对光栅槽的LC振荡辐射进行了估算,发现史密斯-帕塞尔自由电子激光输出频率的模拟值与光栅槽的LC振荡辐射估算值的数量级均为102 GHz,且变化规律上一致。据此推测决定史密斯-帕塞尔自由电子激光输出频率的应该是光栅槽,而不是谐振腔。     

The connected partition lattice of a graph and the reconstruction conjecture

Previously we showed that many invariants of a graph can be computed from its abstract induced subgraph poset, which is the isomorphism class of the induced subgraph poset, suitably weighted by subgraph counting numbers. In this paper, we study the abstract bond lattice of a graph, which is the isomorphism class of the lattice of distinct unlabelled connected partitions of a graph, suitably weighted by subgraph counting numbers. We show that these two abstract posets can be constructed from each other except in a few trivial cases. The constructions rely on certain generalisations of a lemma of Kocay in graph reconstruction theory to abstract induced subgraph posets. As a corollary, trees are reconstructible from their abstract bond lattice. We show that the chromatic symmetric function and the symmetric Tutte polynomial of a graph can be computed from its abstract induced subgraph poset. Stanley has asked if every tree is determined up to isomorphism by its chromatic symmetric function. We prove a counting lemma, and indicate future directions for a study of Stanley's question.     

Theoretical studies of photovoltaic properties of five new silol dithiophene based D2-A-D1-A-D2 donors

Organic solar cell of silol dithiophene based D₂-A-D₁-A-D₂/PC₇₁BM (D: donor part; A: acceptor part; 1 and 2 denote different units) possesses promising power conversion efficiency. Researchers have studied D₂-A-D₁-A-D₂ molecules carefully, including the effects of the different number of terminal thiophenes, the different central moiety (D₁), and the length of the alkyl chain. However, there are few investigations, especially theoretical studies, on the influences of different A (acceptor) units on the properties of D₂-A-D₁-A-D₂ molecule. In the present work, we have designed and modeled five new D₂-A-D₁-A-D₂ (D₂ = bithiophene and D₁ = silol dithiophene) donors by changing A units (A = diketopyrrolopyrrole, naphtho[1,2-c:5,6-c′]bis[1,2,5]thiadiazole, 5-fluoro-2,1,3-benzoselenadiazole, benzobisthiadiazole, and thiazolo[5,4-d]thiazole). We have applied density functional theory (DFT) and time-dependent DFT to predict their ground-state electronic structures and the UV–vis spectra, and the open circuit voltages (Vocs) of organic solar cells of D₂-A-D₁-A-D₂/PC₇₁BM. Based on the calculated results, we find that bithiophene thiazolo[5,4-d]thiazole siloldithiophene (BTTS) (D₂ = bithiophene, A = thiazolo[5,4-d]thiazole, D₁ = silol dithiophene) possesses the highest lowest unoccupied molecular orbital (−2.60 eV) and the lowest highest occupied molecular orbital (−5.33 eV) energies, and the strongest absorption in the visible region. Besides, the solar cell of BTTS/PC₇₁BM has the highest Voc of 1.02 V. These results indicate that it may be a promising donor. In contrast, bithiophene benzobisthiadiazole siloldithiophene (BBBS) (A = benzobisthiadiazole) has low absorption strength in the visible region, which indicates that it may not be a suitable donor material.