CrC^r-right equivalence of analytic functions

Let $f,g:(\mathbb{R}^n,0)\rightarrow (\mathbb{R},0)$ be analytic functions. We will show that if $\nabla f(0)=0$ and $g-f \in (f)^{r+2}$ then $f$ and $g$ are $C^r$-right equivalent, where $(f)$ denote ideal generated by $f$ and $r\in \mathbb{N}$.Comment: 9 pages. Main result has been significantly improve

Muir Quartet, November 9, 1995

This is the concert program of the Muir Quartet performance on Thursday, November 9, 1995 at 8:00 p.m., at the Tsai Performance Center, 685 Commonwealth Avenue, Boston, Massachusetts. Works performed were String Quartet in C major, K. 465 "Dissonant" by Wolfgang Amadeus Mozart, String Quartet No. 1 "Kreutzer Sonata" by Leos Janacek, and Piano Quintet in C minor, Op. 115 by Gabriel Fauré. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

A Generalization of Aztec Diamond Theorem, Part II

The author gave a proof of a generalization of the Aztec diamond theorem for a family of $4$-vertex regions on the square lattice with southwest-to-northeast diagonals drawn in (Electron. J. Combin., 2014) by using a bijection between tilings and non-intersecting lattice paths. In this paper, we use Kuo graphical condensation to give a new proof.Comment: 11 pages and 7 figure

Proof of Blum's conjecture on hexagonal dungeons

Matt Blum conjectured that the number of tilings of the Hexagonal Dungeon of sides $a,\ 2a,\ b,\ a,\ 2a,\ b$ (where $b\geq 2a$) is $13^{2a^2}14^{\lfloor\frac{a^2}{2}\rfloor}$ (J. Propp, New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999). In this paper we present a proof for this conjecture using Kuo's Graphical Condensation Theorem (E. Kuo, Applications of Graphical Condensation for Enumerating Matchings and Tilings, Theoretical Computer Science, 2004).Comment: 30 page

Muir String Quartet: A Program of Last Pieces

This is the concert program of the Muir String Quartet performance on Friday, January 17, 1997 at 8:00 p.m., at the Tsai Performance Center, 685 Commonwealth Avenue. Works performed were Quartet in F major, Op. 135 by Ludwig van Beethoven, Sonata for Viola and Piano, Op. 147 by Dmitri Shostakovich, and String Quintet in C major, Op. Posth. 163, D. 956 by Franz Schubert. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

Nata Bob v. Kuo

USDC for the District of New Jerse

Effect of Lipid Composition on Nanostructured Lipid Carrier (NLC) on Ubiquinone Effectiveness as an Anti-aging Cosmetics

The purpose of this research is to determine the optimum composition of solid lipid and liquid lipid in order to increase the penetration and effectiveness of Q10 as antioxidant in anti-aging cosmetics. Solid lipid and liquid lipid used in this study were cetyl palmitate and caprylic, which were combined to four (4) different ratios, namely 10:0; 9:1; 7:3 and 5:5. NLC Q10 in this study was produced by high shear homogenization method at 3400 rpm for 5 cycles and at 24000 for 1 cycle. The fourth formula was evaluated in term of characteristics, penetration and effectiveness. From the pH test , it was known that all formulas met the skin pH range (4.0-6.0). For the particle size test , all formulas (NLC 1 - NLC 4) were in the range from 269.13 to 354.77 nm with NLC 3 (7: 3) had the smallest particle size. The results of viscosity and surface tension test were also consistent with the theory, where the addition of liquid lipid reduced viscosity and surface tension of the system. The entrapment efficiency (EE) demonstrated the EE of NLC 1: 22.24%; NLC 2: 24.71%; NLC 3: 58.21% and NLC 4:36.94%. The penetration test showed all systems were able to penetrate the dermis layer at the 5th hour. NLC 3 (7:3) had more rapid onset, while the NLC Q10 with the ratio of lipid 9:1, had slower onset of action but can penetrate farther than the other NLC Q10 system. The result of Q10 effectiveness test showed NLC 2 (9:1) has lowest total macrophage (23.33) and very dense collagen observation (score : 4). From this research, it can be concluded that NLC 2 (9:1) had the most optimal lipid composition to increase the penetration and effectiveness of Q10 as an antioxidant in anti-aging cosmetics