Mass Matrices in E6 Unification

We study a supersymmetric E6 grand unified model in which the SU(5) 5^* components are twisted in the third generation 27. Supplementing the adjoint Higgs field to a model analyzed previously, we calculate the mass matrices for the up and down quarks and charged leptons. Although the number of free parameters is less than that of observables, an overall fitting to the observed masses and mixing angles is shown to be possible. Most notably, we find two novel, parameter-independent relations between the lepton 2-3 mixing angle and the quark masses and CKM mixing angles that are in good agreement with the large lepton mixing recently observed.Comment: 33 pages, 5 figures, typos correcte

Hierarchical Mass Matrices in a Minimal SO(10) Grand Unification I

We consider a minimal SO(10) unified model with horizontal Peccei-Quinn symmetry. The hierarchical structure of quark-lepton mass matrices is naturally implemented by the remnants of certain irrelevant terms. Georgi-Jarlskog relations are also realized due to the horizontal symmetry.Comment: phyzzx and tables, 15 pages, KUNS 125

Exact shock solution of a coupled system of delay differential equations: a car-following model

In this paper, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called {\it the car-following model}. We use the Hirota method, originally developed in order to solve soliton equations. %While, with a periodic boundary condition, this system has % a traveling-wave solution given by elliptic functions. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with a periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

Useful Measurement of Glucose Variability by Flash Glucose Monitoring (FGM) with the Efficacy of Sodium-Glucose Cotransporter 2 (SGLT2) Inhibitor

Diabetes has been a crucial medical and social problem worldwide. For adequate nutritional therapy, there have been discussions concerning Calorie Restriction (CR) and Low Carbohydrate Diet (LCD). We have investigated glucose variability of diabetic patients applying CR, LCD, continuous glucose monitoring (CGM) and applied FreeStyle Libre which is flash glucose monitoring (FGM). The patient is a 40-year-old female with type 2 diabetes mellitus (T2DM), who showed BMI 20.7, postprandial blood glucose 257 mg/dL. HbA1c 12.1%, Glycoalbumin 31.6% (11.6-16.4), serum C-peptide 2.0 ng/ml and unremarkable data of liver function, renal, lipids. She was provided the intervention of three stages, which are i) CR with 60% carbohydrate in Day 1-2, ii) LCD meal with 12% carbohydrate in Day 3-5; iii) LCD + Sodium-glucose cotransporter 2 (SGLT2) inhibitor (Ipragliflozin L-Proline 50mg) in Day 6-12. The glucose profile was measured by FreeStyle Libre Pro (Abbott) for 14 days. The daily profile of blood glucose was abruptly decreased on Day 6. Time percentage of satisfactory blood glucose 70-180 mg/dL (/24h) was 0%, 0%, 2%, 14%, 0%, 54%, 100% in Day 1-7, respectively. These results suppose the acute clinical efficacy of SGLT2 inhibitor, and this report would become a reference for future diabetic practice and research

Evaluating Insulin/Glucose Ratio Using Breakfast of Calorie Restriction Meal for Type 2 Diabetes Mellitus

Background: Type 2 diabetes mellitus (T2DM) has been a medical and social problem worldwide. For nutritional therapy, Low Carbohydrate Diet (LCD) and Calorie restriction (CR) have discussed for long, where authors continued clinical research. Subjects and Methods: Subjects were 68 patients with T2DM with 62.1 years on average. Methods included i) standard CR was provided a day with 1400 kcal and 60% of carbohydrate, ii) measurement of daily profile of blood glucose, iii) insulinogenic index (IGI) (0-30 mins) exam for breakfast including 70g of carbohydrate, iv) calculation of IGI by delta and Area Under the Curves(AUC). Results: Basal data revealed that HbA1c 7.9%, fasting glucose 163 mg/dL, average glucose in a day 210 mg/dL, M value 117 in the median. Increment of glucose/IRI was 48.0 mg/dL/8.6 μU/mL, respectively. Delta or AUC ratio of IGI was 0.14[0.08-0.26] and 3.3[2.5-5.2], respectively. There were significant correlations between M value and Delta or AUC ratio, with a higher coefficient in the latter. Discussion and Conclusion: IGI study in Meal Tolerance Test (MTT) would be useful for pancreas function evaluation. AUC ratio method has superiority than Delta ratio with higher correlation coefficient. Current results could be the fundamental data for the related range of research, and further development will be expected

Energy Dissipation Burst on the Traffic Congestion

We introduce an energy dissipation model for traffic flow based on the optimal velocity model (OV model). In this model, vehicles are defined as moving under the rule of the OV model, and energy dissipation rate is defined as the product of the velocity of a vehicle and resistant force which works to it.Comment: 15 pages, 19 Postscript figures. Reason for replacing: This is the submitted for

Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow

Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by elliptic theta function. Each solution of the set describes a density wave with definite number of car-bunches in the circuit. By the numerical simulation, we observe a transition process from a uniform flow to the one-bunch analytic solution, which seems to be an attractor of the system. In the process, the system shows a series of cascade transitions visiting the configurations closely similar to the higher multi-bunch solutions in the set.Comment: revtex, 7 pages, 5 figure