scholarly journals Marstrand-type Theorems for the Counting and Mass Dimensions in ℤ

2016 ◽  
Vol 25 (5) ◽  
pp. 700-743 ◽  
Author(s):  
DANIEL GLASSCOCK
Keyword(s):  
Recent Work ◽  
Orthogonal Projection ◽  
Side Length ◽  
Orthogonal Projections ◽  
Mass Dimension ◽  
Image Position ◽  
Almost All

The counting and (upper) mass dimensions of a set A ⊆ $\mathbb{R}^d$ are $$D(A) = \limsup_{\|C\| \to \infty} \frac{\log | \lfloor A \rfloor \cap C |}{\log \|C\|}, \quad \smash{\overline{D}}\vphantom{D}(A) = \limsup_{\ell \to \infty} \frac{\log | \lfloor A \rfloor \cap [-\ell,\ell)^d |}{\log (2 \ell)},$$ where ⌊A⌋ denotes the set of elements of A rounded down in each coordinate and where the limit supremum in the counting dimension is taken over cubes C ⊆ $\mathbb{R}^d$ with side length ‖C‖ → ∞. We give a characterization of the counting dimension via coverings: $$D(A) = \text{inf} \{ \alpha \geq 0 \mid {d_{H}^{\alpha}}(A) = 0 \},$$ where $${d_{H}^{\alpha}}(A) = \lim_{r \rightarrow 0} \limsup_{\|C\| \rightarrow \infty} \inf \biggl\{ \sum_i \biggl(\frac{\|C_i\|}{\|C\|} \biggr)^\alpha \ \bigg| \ 1 \leq \|C_i\| \leq r \|C\| \biggr\}$$ in which the infimum is taken over cubic coverings {Ci} of A ∩ C. Then we prove Marstrand-type theorems for both dimensions. For example, almost all images of A ⊆ $\mathbb{R}^d$ under orthogonal projections with range of dimension k have counting dimension at least min(k, D(A)); if we assume D(A) = D(A), then the mass dimension of A under the typical orthogonal projection is equal to min(k, D(A)). This work extends recent work of Y. Lima and C. G. Moreira.

Projection theorems for box and packing dimensions

1996 ◽  
Vol 119 (2) ◽  
pp. 287-295 ◽  
Author(s):  
K. J. Falconer ◽  
J. D. Howroyd
Keyword(s):  
Orthogonal Projection ◽  
Packing Dimension ◽  
Analytic Subset ◽  
Box Counting ◽  
Packing Dimensions ◽  
Image Position ◽  
Almost All ◽  
Projection Theorems

AbstractWe show that if E is an analytic subset of ℝn thenfor almost all m–dimensional subspaces V of ℝn, where projvE is the orthogonal projection of E onto V and dimp denotes packing dimension. The same inequality holds for lower and upper box counting dimensions, and these inequalities are the best possible ones.

The packing dimension of projections and sections of measures

1996 ◽  
Vol 119 (4) ◽  
pp. 695-713 ◽  
Author(s):  
Kenneth J. Falconer ◽  
Pertti Mattila
Keyword(s):  
Probability Measure ◽  
Orthogonal Projection ◽  
Packing Dimension ◽  
Image Position ◽  
Almost All

AbstractWe show that for a probability measure μ on ℝnfor almost all m–dimensional subspaces V, provided dimH μ≤m. Here projv denotes orthogonal projection onto V, and dimH and dimp denote the Hausdorff and packing dimension of a measure. In the case dimH μ > m we show that at μ-almost all points x the slices of μ by almost all (n − m)-planes Vx through x satisfyWe give examples to show that these inequalities are sharp.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

Physicochemical and bacteriological characterization of hospital effluents and their impact on the environment

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Human Health ◽  
Fecal Coliforms ◽  
Chemical Pollution ◽  
Hospital Effluents ◽  
Biological Contaminants ◽  
Almost All ◽  
Direct Discharge ◽  
Significant Chemical

Liquid effluents discharged by hospitals may contain chemical and biological contaminants whose main source is the different substances used for the treatment of patients. This type of rejection can present a sanitary potentially dangerous risk for human health and can provoke a strong degradation of diverse environmental compartments mainly water and soils. The present study focuses on the quality of the liquid effluents of Hassani Abdelkader’s hospital of Sidi Bel-Abbes (West of Algeria). The results reveal a significant chemical pollution (COD: 879 mgO2/L, BOD5: 850 mgO2/L, NH4+ : 47.9 mg/l, NO2- : 4.2 mg/l, NO3- : 56.8 mg/l with respect to WHO standard of 90 mgO2/L, 30 mgO2/L, 0.5 mg/l, 1 mg/l and 1 mg/l respectively). However, these effluents are biodegradable since the ratio COD/BOD5 do not exceeded the value of 2 in almost all samples. The presence of pathogen germs is put into evidence such as pseudomonas, the clostridium, the staphylococcus, the fecal coliforms and fecal streptococcus. These results show that the direct discharge of these effluents constitutes a major threat to human health and the environment.

scholarly journals Stoichiometry and compositional plasticity of the yeast nuclear pore complex revealed by quantitative fluorescence microscopy

2018 ◽  
Vol 115 (17) ◽  
pp. E3969-E3977 ◽  
Author(s):  
Sasikumar Rajoo ◽  
Pascal Vallotton ◽  
Evgeny Onischenko ◽  
Karsten Weis
Keyword(s):  
Nuclear Pore Complex ◽  
Yeast Cells ◽  
Nuclear Pore ◽  
Altered Expression ◽  
Copy Numbers ◽  
Quantitative Image ◽  
Multiple Copies ◽  
Almost All ◽  
High Degree

The nuclear pore complex (NPC) is an eightfold symmetrical channel providing selective transport of biomolecules across the nuclear envelope. Each NPC consists of ∼30 different nuclear pore proteins (Nups) all present in multiple copies per NPC. Significant progress has recently been made in the characterization of the vertebrate NPC structure. However, because of the estimated size differences between the vertebrate and yeast NPC, it has been unclear whether the NPC architecture is conserved between species. Here, we have developed a quantitative image analysis pipeline, termed nuclear rim intensity measurement (NuRIM), to precisely determine copy numbers for almost all Nups within native NPCs of budding yeast cells. Our analysis demonstrates that the majority of yeast Nups are present at most in 16 copies per NPC. This reveals a dramatic difference to the stoichiometry determined for the human NPC, suggesting that despite a high degree of individual Nup conservation, the yeast and human NPC architecture is significantly different. Furthermore, using NuRIM, we examined the effects of mutations on NPC stoichiometry. We demonstrate for two paralog pairs of key scaffold Nups, Nup170/Nup157 and Nup192/Nup188, that their altered expression leads to significant changes in the NPC stoichiometry inducing either voids in the NPC structure or substitution of one paralog by the other. Thus, our results not only provide accurate stoichiometry information for the intact yeast NPC but also reveal an intriguing compositional plasticity of the NPC architecture, which may explain how differences in NPC composition could arise in the course of evolution.

scholarly journals On the supposed first stage larva of Leptohylemyia coarctata, Fall.

1917 ◽  
Vol 8 (2) ◽  
pp. 121-123 ◽  
Author(s):  
D. Keilin
Keyword(s):  
Life History ◽  
Recent Work ◽  
European Countries ◽  
Stage Larva ◽  
History Of ◽  
Almost All

It has been well known since the studies of Taschenberg (1864–1872) that the larvae of Leptohylemyia coarctata, Fall., attack wheat and rye. The damage due to this fly has been observed many times in almost all European countries, and many papers have been devoted to its life-history. Of these papers the most important are those of E. Ormerod (1882–1895), S. Rostrup (1905–1911), T. Hedlund (1906- 1907), P. Marchal (1909) and finally the recent work of Kurdjumov (1914).

Study of Painting Materials and Techniques in the 18th Century St.Athanasius Church in Moschopolis, Albania

2007 ◽  
Vol 1047 ◽  
Author(s):  
Eleni Pavlidou ◽  
N. Civici ◽  
E. Caushi ◽  
L. Anastasiou ◽  
T. Zorba ◽  
...  
Keyword(s):  
18Th Century ◽  
Orthodox Church ◽  
Wall Paintings ◽  
Cultural Center ◽  
Green Earth ◽  
Almost All ◽  
The City ◽  
The Church ◽  
Compositional Characterization

AbstractIn this paper are presented the studies of the paint materials and the technique used in 18th century wall paintings, originated from the orthodox church of St Athanasius, in the city of Maschopolis, a flourishing economical and cultural center, in Albania. The church was painted in 1745 by Konstantinos and Athanasios Zografi, and during the last years, restoration activities are being performed at the church. Samples that included plasters and pigments of different colors were collected from important points of the wall paintings. Additionally, as some parts of the wall-paintings were over-painted, the analysis was extended to the compositional characterization of these areas. The identification of the used materials was done by using complementary analytical methods such as Optical Microscopy, Fourier Transform Infrared spectroscopy (FTIR), Scanning Electron Microscopy (SEM-EDS) and X-ray fluorescence (TXRF).The presence of calcite in almost all the pigments is indicative for the use of the fresco technique at the studied areas, while the detection of gypsum and calcium oxalate, indicates an environmental degradation along with a biodegradation. Common pigments used in this area at 15-16th centuries, such as cinnabar, green earth, manganese oxide, carbon black and calcite were identified.

Experimental Study of Ductile Fracture for Non-Aligned Multiple Flaws in a Plate

2009 ◽  
Author(s):  
Katsumasa Miyazaki ◽  
Kunio Hasegawa ◽  
Koichi Saito ◽  
Bostjan Bezensek
Keyword(s):  
Experimental Study ◽  
Ductile Fracture ◽  
Estimation Procedure ◽  
Maximum Load ◽  
Experimental Results ◽  
Collapse Load ◽  
Plate Specimen ◽  
Fracture Tests ◽  
Almost All

The fitness-for-service code requires the characterization of non-aligned multiple flaws for the flaw evaluation, which is performed using a flaw proximity rule. Worldwide almost all codes provide own proximity rule, often with unclear technical bases of the application of proximity rule to ductile fracture. To clarify the appropriate proximity rule for non-aligned multiple flaws in fully plastic fracture, fracture tests on flat plate specimen with non-aligned multiple through wall flaws were conducted at ambient temperature. The emphasis of this study was put on the flaw alignment rule, which determines whether non-aligned flaws are treated as independent or aligned onto the same plane for the purpose of flaw evaluations. The effects of the flaw separation and flaw size on the maximum load were investigated. The experimental results were compared with the estimations of the collapse load using the alignment rules in the ASME Section XI, BS7910 and API 579-1 codes. A new estimation procedure specific to the fully plastic fracture was proposed and compared with the comparison with the experimental results.

scholarly journals Isolation and Characterization of Bacteriophage ZCSE6 against Salmonella spp.: Phage Application in Milk

Biologics ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 164-176
Author(s):  
Abdallah S. Abdelsattar ◽  
Anan Safwat ◽  
Rana Nofal ◽  
Amera Elsayed ◽  
Salsabil Makky ◽  
...  
Keyword(s):  
Pathogenic Bacteria ◽  
Raw Milk ◽  
Salmonella Spp ◽  
Isolation And Characterization ◽  
Food Borne ◽  
Wide Range ◽  
Almost All ◽  
And Control ◽  
Milk And Dairy Products

Food safety is very important in the food industry as most pathogenic bacteria can cause food-borne diseases and negatively affect public health. In the milk industry, contamination with Salmonella has always been a challenge, but the risks have dramatically increased as almost all bacteria now show resistance to a wide range of commercial antibiotics. This study aimed to isolate a bacteriophage to be used as a bactericidal agent against Salmonella in milk and dairy products. Here, phage ZCSE6 has been isolated from raw milk sample sand molecularly and chemically characterized. At different multiplicities of infection (MOIs) of 0.1, 0.01, and 0.001, the phage–Salmonella interaction was studied for 6 h at 37 °C and 24 h at 8 °C. In addition, ZCSE6 was tested against Salmonella contamination in milk to examine its lytic activity for 3 h at 37 °C. The results showed that ZCSE6 has a small genome size (<48.5 kbp) and belongs to the Siphovirus family. Phage ZCSE6 revealed a high thermal and pH stability at various conditions that mimic milk manufacturing and supply chain conditions. It also demonstrated a significant reduction in Salmonella concentration in media at various MOIs, with higher bacterial eradication at higher MOI. Moreover, it significantly reduced Salmonella growth (MOI 1) in milk, manifesting a 1000-fold decrease in bacteria concentration following 3 h incubation at 37 °C. The results highlighted the strong ability of ZCSE6 to kill Salmonella and control its growth in milk. Thus, ZCSE6 is recommended as a biocontrol agent in milk to limit bacterial growth and increase the milk shelf-life.

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