The Sylvester Theorem and the Rogers-Ramanujan Identities over Totally Real Number Fields

In this paper, we prove two identities on the partition of a totally positive algebraic integer over a totally real number field which are the generalization of the Sylvester Theorem and that of the Rogers-Ramanujan Identities. Additionally, we give an another version of generalized Rogers-Ramanujan Identities

The Euler-Glaisher Theorem over Totally Real Number Fields

In this paper, we study the partition theory over totally real number fields. Let $K$ be a totally real number field. A partition of a totally positive algebraic integer $\delta$ over $K$ is $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_r)$ for some totally positive integers $\lambda_i$ such that $\delta=\lambda_1+\lambda_2+\cdots+\lambda_r$. We find an identity to explain the number of partitions of $\delta$ whose parts do not belong to a given ideal $\mathfrak a$. We obtain a generalization of the Euler-Glaisher Theorem over totally real number fields as a corollary. We also prove that the number of solutions to the equation $\delta=x_1+2x_2+\cdots+nx_n$ with $x_i$ totally positive or $0$ is equal to that of chain partitions of $\delta$. A chain partition of $\delta$ is a partition $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_r)$ of $\delta$ such that $\lambda_{i+1}-\lambda_i$ is totally positive or $0$

Optimization of Printed Circuit Heat Exchanger Using Exergy Analysis

A printed circuit heat exchanger (PCHE) with zigzag flow channels in a double-faced configuration was optimized to enhance its thermal-hydraulic performance. Using exergy analysis, the objective function was defined as the net exergy gain of the system considering the exergy gain by heat transfer and exergy loss due to friction in the channels. A Reynolds-averaged Navier-Stokes (RANS) analysis and surrogate modeling techniques were used for the optimization. Three geometric variables were selected as the design variables. The objective function was calculated at each design point through RANS analysis in order to construct a response surface surrogate model. Through the optimization, both the thermal and hydraulic performances of the PCHE were improved with respect to the reference geometry by suppressing flow separation in the channels

A novel approach to fabricate carbon-sphere-intercalated holey graphene electrode for high-energy-density electrochemical capacitors

Desirable porous structure and huge ion-accessible surface area are crucial for rapid electronic and ionic pathway electrodes in high-performance graphene-based electrochemical capacitors. However, graphene nanosheets tend to aggregate and restack because of van der Waals interaction among graphene sheets, resulting in the loss of ion-accessible surface area and unsatisfactory electrochemical performance. To resolve this daunting challenge, a novel approach is developed for the self-assembly of holey graphene sheets intercalated with carbon spheres (H-GCS) to obtain freestanding electrodes by using a simple vacuum filtration approach and a subsequent KOH activation process. Through the introduction of carbon spheres as spacers, the restacking of reduced graphene oxide (rGO) sheets during the filtration process is mitigated efficiently. Pores on rGO sheets produced by subsequent KOH activation also provide rapid ionic diffusion kinetics and high ion-accessible electrochemical surface area, both of which favor the formation of electric double-layer capacitance. Furthermore, a higher degree of graphitization of CSs in H-GCS thin film improves the electrical conductivity of the H-GCS electrode. The H-GCS electrode exhibits 207.1 F g−1 of specific capacitance at a current density of 1 A g−1 in 6 M KOH aqueous electrolyte. Moreover, the symmetric electrochemical capacitor assembled with H-GCS electrodes and organic electrolyte is capable of delivering a maximum energy density of 29.5 Wh kg−1 and a power density of 22.6 kW kg−1

Chemocauterization of Congenital Fistula from the Accessory Parotid Gland

Congenital sialo-cutaneous fistula arising from the accessory parotid gland is extremely rare. Although the fistula tract can be successfully excised after making a skin incision along the skin tension line around the fistula opening, a facial scar inevitably remains. We here report a case of sialo-cutaneous fistula that was treated with chemocauterization with trichloroacetic acid (TCA). TCA cauterization is an easy and effective option for the treatment of congenital fistula from an accessory parotid gland, especially from the aesthetic point of view

A New Capacitive Displacement Sensor with High Accuracy and Long-Range",

ABSTRACT A new capacitive displacement sensor is designed and fabricated for measurement of a large displacement with very high accuracy. This sensor is a kind of linear encoder with an array of micro electrodes made by micromachining processes. The two patterned electrodes on the sensor substrates are assembled facing each other after being coated with thin dielectric film. Due to the thin dielectric film, it is highly sensitive to displacement but minimizes expected misalignments such as a tilting error. The sensor fabricated as a sample has a grating of electrodes with a width of 100µm, which is coated with a Diamond-Like Carbon(DLC) film 0.8 µm thick. The proposed sensor was tested to conclude that its resolution is 9.07 nanometers for the measuring range of 15 millimeters and that the linearity error is expected to be less than 0.02% throughout the measurable range

Pulsed radiofrequency lesioning for treatment of chronic breast neuropathic pain after breast reduction -A case report-

Breast surgery is a common procedure performed in women. Many women who undergo breast surgery suffer from ill-defined pain syndromes. A nerve block is used in the treatment of the acute and chronic pain, but the effectiveness of the treatment has been limited because of its short duration. Recently, the advent of pulsed radiofrequency lesioning (PRF) has proved a successful treatment for chronic refractory pain involving the peripheral nerves. We experienced a case of a 52-year-old female patient complaining of chronic breast neuropathic pain after breast reduction, which was relieved after PRF lesioning of the 4th thoracic spinal nerve and its root