scholarly journals Drawing the almost convex set in an integer grid of minimum size

2017 ◽  
Vol 65 ◽  
pp. 1-11
Author(s):  
Frank Duque ◽  
Ruy Fabila-Monroy ◽  
Carlos Hidalgo-Toscano ◽  
Pablo Pérez-Lantero
Keyword(s):  
Convex Set ◽  
Minimum Size ◽  
Almost Convex

Preparation of integrated circuits for TEM electromigration in situ studies

1986 ◽  
Vol 44 ◽  
pp. 882-883
Author(s):  
J. V. Maskowitz ◽  
W. E. Rhoden ◽  
D. R. Kitchen ◽  
R. E. Omlor ◽  
P. F. Lloyd
Keyword(s):  
Integrated Circuits ◽  
Crystallographic Orientation ◽  
Silicon Wafers ◽  
Minimum Size ◽  
Test Vehicle ◽  
In Situ Studies ◽  
Boron Doped ◽  
Doped Silicon ◽  
Drill Holes

The fabrication of the aluminum bridge test vehicle for use in the crystallographic studies of electromigration involves several photolithographic processes, some common, while others quite unique. It is most important to start with a clean wafer of known orientation. The wafers used are 7 mil thick boron doped silicon. The diameter of the wafer is 1.5 inches with a resistivity of 10-20 ohm-cm. The crystallographic orientation is (111).Initial attempts were made to both drill and laser holes in the silicon wafers then back fill with photoresist or mounting wax. A diamond tipped dentist burr was used to successfully drill holes in the wafer. This proved unacceptable in that the perimeter of the hole was cracked and chipped. Additionally, the minimum size hole realizable was > 300 μm. The drilled holes could not be arrayed on the wafer to any extent because the wafer would not stand up to the stress of multiple drilling.

Transplantation of coral fragment, Acropora formosa (Scleractinia)

2014 ◽  
pp. 1
Author(s):  
Hanny Tioho ◽  
Maykel A.J Karauwan
Keyword(s):  
Fragment Size ◽  
Observation Time ◽  
Minimum Size ◽  
Average Growth Rate ◽  
Average Growth ◽  
Significant Difference ◽  
Acropora Formosa ◽  
Survival And Growth ◽  
One Way Anova ◽  
Better Than

The minimum size of coral transplants, Acropora formosa, was assessed to support their survival and growth. For this, 150 coral fragments of different sizes (5, 10, 15 cm) were transplanted close to the donor colony. Their survivorship and growth were observed for 12 months. At the end of the observation time, 90% of 15 cm-transplanted coral fragments survived, while the others (10cm and 5 cm) did 86% and 82% respectively. The average growth rate of 5 cm-coral fragments was 0.860 cm/month, while 10 and 15 cm-fragments were 0.984 cm/month and 1.108 cm/month respectively. One-way ANOVA showed that there was significant difference (p<0.05) among the three (5, 10, 15 cm) transplant initial sizes in which the longest fragment size tended to survive longer than the smaller one.  However, the smaller transplants grew better than the bigger one, 10.318 cm/year (206%) for 5 cm-transplant, 11.803 cm/year (118%) for 10 cm-transplant, and 13.299 cm/year (89%) for 15 cm-transplant, respectively. Ukuran minimal fragmen karang Acropora formosa yang ditransplantasi diduga untuk mendukung ketahanan hidup dan pertumbuhannya. Untuk itu, 150 fragmen karang ditransplantasi ke lokasi yang berdekatan dengan koloni induknya.  Ketahanan hidup dan pertumbuhan semua fragmen karang yang ditransplantasi diamati selama 12 bulan.  Pada akhir pengamatan, 90% dari fragmen karang berukuran 15 cm yang ditransplantasi dapat bertahan hidup, sedangkan yang lainnya (ukuran 10 cm dan 5 cm) masing-masing sebesar 86% dan 82%.  Rata-rata laju pertumbuhan fragmen karang dengan ukuran awal 5 cm adalah 0,860 cm/bulan, sedangkan ukuran fragmen 10 dan 15 cm masing-masing adalah 0,984 cm/bulan and 1,108 cm/bulan. ANOVA satu arah menunjukkan adanya perbedaan yang nyata (p<0.05) antara ketiga ukuran fragmen yang berbeda, di mana ukuran fragmen karang yang lebih panjang cenderung mempunyai ketahanan hidup yang lebih baik. Namun demikian, ukuran transplant yang lebih kecil memiliki pertumbuhan lebih baik dibandingkan dengan ukuran yang lebih besar, yakni10,318 cm/tahun (206%) untuk transplant berukuran 5 cm, 11,803 cm/tahun (118%) untuk 10 cm, dan 13,299 cm/tahun (89%) untuk ukuran 15 cm.

On a Two-Sided Turán Problem

10.37236/1735 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Dhruv Mubayi ◽  
Yi Zhao
Keyword(s):  
Minimum Size ◽  
Turan Problem ◽  
Turan Problems ◽  
Turán Problem ◽  
Positive Integers

Given positive integers $n,k,t$, with $2 \le k\le n$, and $t < 2^k$, let $m(n,k,t)$ be the minimum size of a family ${\cal F}$ of nonempty subsets of $[n]$ such that every $k$-set in $[n]$ contains at least $t$ sets from ${\cal F}$, and every $(k-1)$-set in $[n]$ contains at most $t-1$ sets from ${\cal F}$. Sloan et al. determined $m(n, 3, 2)$ and Füredi et al. studied $m(n, 4, t)$ for $t=2, 3$. We consider $m(n, 3, t)$ and $m(n, 4, t)$ for all the remaining values of $t$ and obtain their exact values except for $k=4$ and $t= 6, 7, 11, 12$. For example, we prove that $ m(n, 4, 5) = {n \choose 2}-17$ for $n\ge 160$. The values of $m(n, 4, t)$ for $t=7,11,12$ are determined in terms of well-known (and open) Turán problems for graphs and hypergraphs. We also obtain bounds of $m(n, 4, 6)$ that differ by absolute constants.

Formulation, Optimization,and Ex-Vivo Evaluation of Novel Lipid Carriers for Enhanced Transdermal Delivery of Hydroquinone

2020 ◽  
Vol 12 ◽  
Author(s):  
Shivani Verma ◽  
Sukhjinder Kaur ◽  
Lalit Kumar
Keyword(s):  
Ex Vivo ◽  
Skin Permeation ◽  
Topical Delivery ◽  
Gelling Agent ◽  
Minimum Size ◽  
Prolonged Release ◽  
Freeze Dried ◽  
Ft Ir ◽  
Ir Analysis ◽  
Skin Retention

Background: HQ is used for hyper-pigmentation treatment using conventional creams and gels. These formulations show various disadvantages like poor skin permeation, allergic reactions, and repeated use decreasing patient compliance. Objectives: The present work involved formulation, statistical optimization, and characterization of nanostructured lipid carriers (NLCs) for efficient topical delivery of hydroquinone (HQ) for hyperpigmentation treatment. Methods: The NLCs were optimized exploring Box–Behnken design (BBD) using three independent variables and two dependent variables. Formulation having the minimum size and maximum drug entrapment was considered as optimized formulation. Optimized formulation was evaluated for drug release followed by its freeze-drying. The freeze-dried formulation was subjected to differential scanning calorimetry (DSC) analysis, X-raydiffraction (XRD) analysis, and Fourier transform-infrared spectroscopy (FT-IR) analysis. Furthermore, NLCs based gel was prepared by using Carbopol 934 as a gelling agent. NLCs based gel was evaluated for skin permeation, skin retention, and skin distribution (through confocal microscopic analysis) using pig ear skin. Results: Optimized NLCs showed smaller particle size [(271.9 ± 9) nm], high drug entrapment [(66.4 ± 1.2) %], tolerable polydispersity index (PDI) (0.221 ± 0.012), and zeta potential [(-25.9± 1.2) mV]. The FT-IR analysis revealed excellent compatibility between HQ and other excipients. The Carbopol 934 gel containing NLCs showed high transdermal flux [(163 ± 16.2) μg/cm2/h], permeability coefficient (0.0326 ± 0.0016), and skin permeation enhancement ratio (3.7 ± 0.4) compared to marketed cream of HQ. The results of confocal microscopic (CLSM) analysis revealed the accumulation of optimized NLCs in the lower epidermal layers of skin. Conclusion: NLCs based gel was considered effective in the topical delivery of HQ to treat hyper-pigmentation due high skin permeation, skin retention, and prolonged release of HQ.

Sharpening an Estimate of the Size of the Sumset of a Convex Set

2020 ◽  
Vol 107 (5-6) ◽  
pp. 984-987
Author(s):  
K. I. Ol’mezov
Keyword(s):  
Convex Set

The Oxford Handbook of IPOs

2018 ◽  
Keyword(s):  
United States ◽  
Initial Public Offerings ◽  
Financial Regulation ◽  
Large Body ◽  
Public Information ◽  
The United States ◽  
Minimum Size ◽  
Stock Exchanges ◽  
Public Offerings ◽  
Firm’S Life Cycle

Firms generally begin as privately owned entities. When they grow large enough, the decision to go public and its consequences are among the most crucial times in a firm’s life cycle. The first time a firm is a reporting issuer gives rise to tremendous responsibilities about disclosing public information and accountability to a wide array of retail shareholders and institutional investors. Initial public offerings (IPOs) offer tremendous opportunities to raise capital. The economic and legal landscape for IPOs has been rapidly evolving across countries. There have been fewer IPOs in the United States in the aftermath of the 2007–2009 financial crisis and associated regulatory reforms that began in 2002. In 1980–2000, an average of 310 firms went public every year, while in 2001–2014 an average of 110 firms went public every year. At the same time, there are so many firms that seek an IPO in China that there has been a massive waiting list of hundreds of firms in recent years. Some countries are promoting small junior stock exchanges to go public early, and even crowdfunding to avoid any prospectus disclosure. Financial regulation of analysts and investment banks has been evolving in ways that drastically impact the economics of going public—in some countries, such as the United States, drastically increasing the minimum size of a company before it can expect to go public. This Handbook not only systematically and comprehensively consolidates a large body of literature on IPOs, but provides a foundation for future debates and inquiry.

scholarly journals Metric Dimension Parameterized By Treewidth

Algorithmica ◽  
2021 ◽  
Author(s):  
Édouard Bonnet ◽  
Nidhi Purohit
Keyword(s):  
Computable Function ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Minimum Size ◽  
Metric Dimension ◽  
Resolving Set ◽  
Input Graph ◽  
Outerplanar Graphs ◽  
Bounded Treewidth ◽  
Fpt Algorithm

AbstractA resolving set S of a graph G is a subset of its vertices such that no two vertices of G have the same distance vector to S. The Metric Dimension problem asks for a resolving set of minimum size, and in its decision form, a resolving set of size at most some specified integer. This problem is NP-complete, and remains so in very restricted classes of graphs. It is also W[2]-complete with respect to the size of the solution. Metric Dimension has proven elusive on graphs of bounded treewidth. On the algorithmic side, a polynomial time algorithm is known for trees, and even for outerplanar graphs, but the general case of treewidth at most two is open. On the complexity side, no parameterized hardness is known. This has led several papers on the topic to ask for the parameterized complexity of Metric Dimension with respect to treewidth. We provide a first answer to the question. We show that Metric Dimension parameterized by the treewidth of the input graph is W[1]-hard. More refinedly we prove that, unless the Exponential Time Hypothesis fails, there is no algorithm solving Metric Dimension in time $$f(\text {pw})n^{o(\text {pw})}$$ f ( pw ) n o ( pw ) on n-vertex graphs of constant degree, with $$\text {pw}$$ pw the pathwidth of the input graph, and f any computable function. This is in stark contrast with an FPT algorithm of Belmonte et al. (SIAM J Discrete Math 31(2):1217–1243, 2017) with respect to the combined parameter $$\text {tl}+\Delta$$ tl + Δ , where $$\text {tl}$$ tl is the tree-length and $$\Delta$$ Δ the maximum-degree of the input graph.

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