Study on Correlation of Physical and Mechanical Properties Indexex of Cohesive Soil in Hilly and Plain Region along the Yangtze River in Anhui Province

In this paper, a large number of geotechnical engineering survey data are collected in hilly and plain region along the Yangtze River in Anhui Province. Based on the statistical analysis and calculation of the experimental data of physical and mechanical properties of cohesive soils (the main quaternary soil layers in the area), the correlation between the liquidity index and water content and other physical and mechanical properties indexes are analyzed, and the fitting regression is carried out respectively. The results show that the liquidity index (IL)) and water content (w) are highly correlated with cohesion (C), compression modulus (Es), compression coefficient (α), natural density (ρ), void ratio (e), and the regression equations have high goodness of fit and good fitting effect; In addition, the fitting regression equations of water content, void ratio and natural density are compared with the theoretical calculation formula, it is found that the calculation results are close, which proves that the fitting regression equations are reliable and can be used in engineering practice.

Occurrence of Double Bond in π-Aromatic Rings: An Easy Way to Design Doubly Aromatic Carbon-Metal Structures

A chemical bonding of several metallabenzenes and metallabenzynes was studied via an adaptive natural density partitioning (AdNDP) algorithm and the induced magnetic field analysis. A unique chemical bonding pattern was discovered where the M=C (M: Os, Re) double bond coexists with the delocalized 6c-2e π-bonding elements responsible for aromatic properties of the investigated complexes. In opposition to the previous description where 8 delocalized π-electrons were reported in metallabenzenes and metallabenzynes, we showed that only six delocalized π-electrons are present in those molecules. Thus, there is no deviation from Hückel’s aromaticity rule for metallabenzynes/metallabenzenes complexes. Based on the discovered bonding pattern, we propose two thermodynamically stable novel molecules that possess not only π-delocalization but also retain six σ-delocalized electrons, rendering them as doubly aromatic species. As a result, our investigation gives a new direction for the search for carbon-metal doubly aromatic molecules.

The Proof of a Conjecture on the Density of Sets Related to Divisibility Properties of z(n)

Let (Fn)n be the sequence of Fibonacci numbers. The order of appearance (in the Fibonacci sequence) of a positive integer n is defined as z(n)=min{k≥1:n∣Fk}. Very recently, Trojovská and Venkatachalam proved that, for any k≥1, the number z(n) is divisible by 2k, for almost all integers n≥1 (in the sense of natural density). Moreover, they posed a conjecture that implies that the same is true upon replacing 2k by any integer m≥1. In this paper, in particular, we prove this conjecture.

The Proof of a Conjecture Related to Divisibility Properties of z(n)

The order of appearance of n (in the Fibonacci sequence) z(n) is defined as the smallest positive integer k for which n divides the k—the Fibonacci number Fk. Very recently, Trojovský proved that z(n) is an even number for almost all positive integers n (in the natural density sense). Moreover, he conjectured that the same is valid for the set of integers n ≥ 1 for which the integer 4 divides z(n). In this paper, among other things, we prove that for any k ≥ 1, the number z(n) is divisible by 2k for almost all positive integers n (in particular, we confirm Trojovský’s conjecture).

Analysis of Local and Global Aromaticity in Si3C5 and Si4C8 Clusters. Aromatic Species Containing Planar Tetracoordinate Carbon

The minimum energy structures of the Si3C5 and Si4C8 clusters are planar and contain planar tetracoordinate carbons (ptCs). These species have been classified, qualitatively, as global (π) and local (σ) aromatics according to the adaptive natural density partitioning (AdNDP) method, which is an orbital localization method. This work evaluates these species’ aromaticity, focusing on confirming and quantifying their global and local aromatic character. For this purpose, we use an orbital localization method based on the partitioning of the molecular space according to the topology of the electronic localization function (LOC-ELF). In addition, the magnetically induced current density is analyzed. The LOC-ELF-based analysis coincides with the AdNDP study (double aromaticity, global, and local). Moreover, the current density analysis detects global and local ring currents. The strength of the global and local current circuit is significant, involving 4n + 2 π- and σ-electrons, respectively. The latter implicates the Si-ptC-Si fragment, which would be related to the 3c-2e σ-bond detected by the orbital localization methods in this fragment.

In Silico Studies on Selected Neutral Molecules, CGa2Ge2, CAlGaGe2, and CSiGa2Ge Containing Planar Tetracoordinate Carbon

Density functional theory (DFT) was used to study the structure, stability, and bonding in some selected neutral pentaatomic systems, viz., CGa2Ge2, CAlGaGe2, and CSiGa2Ge containing planar tetracoordinate carbon. The systems are kinetically stable, as predicted from the ab initio molecular dynamics simulations. The natural bond orbital (NBO) analysis showed that strong electron donation occurs to the central planar carbon atom by the peripheral atoms in all the studied systems. From the nucleus independent chemical shift (NICS) analysis, it is shown that the systems possess both σ- and π- aromaticity. The presence of 18 valence electrons in these systems, in their neutral form, appears to be important for their stability with planar geometries rather than tetrahedral structures. The nature of bonding is understood through the adaptive natural density partitioning analysis (AdNDP), quantum theory of atoms in molecules (QTAIM) analysis, and also via Wiberg bond index (WBI) and electron localization function (ELF).

Analysis of Local and Global Aromaticity in Si3C5 and Si4C8 Clusters. Aromatic Species Containing Planar Tetracoordinate Carbon

The minimum energy structures of the Si3C5 and Si4C8 clusters are planar and contain planar tetracoordinate carbons (ptCs). These species have been classified, qualitatively, as global () and local () aromatics according to the adaptive natural density partitioning (AdNDP) method, which is an orbital localization method. This work evaluates these species' aromaticity, focusing on confirming and quantifying their global and local aromatic character. For this purpose, we use an orbital localization method based on the partitioning of the molecular space according to the topology of the electronic localization function (LOC-ELF). In addition, the magnetically induced current density is analyzed. The LOC-ELF-based analysis coincides with the AdNDP study (double aromaticity, global and local). Besides, the current density analysis detects global and local ring currents. The strength of the global and local current circuit is significant, involving 4n+2 - and -electrons, respectively. The latter implicates the Si-ptC-Si fragment, which would be related to the 3c-2e -bond detected by the orbital localization methods in this fragment.

On the Parity of the Order of Appearance in the Fibonacci Sequence

Let (Fn)n≥0 be the Fibonacci sequence. The order of appearance function (in the Fibonacci sequence) z:Z≥1→Z≥1 is defined as z(n):=min{k≥1:Fk≡0(modn)}. In this paper, among other things, we prove that z(n) is an even number for almost all positive integers n (i.e., the set of such n has natural density equal to 1).

Redesign Geometri Lereng Penambangan Batugamping Kuari C di PT X Kecamatan Palimanan Kabupaten Cirebon Provinsi Jawa Barat

PT X is a cement producer which has a limestone mine in Palimanan District, Cirebon Regency, West Java Province. In the Quarry C limestone mining area there has been an landslide that has resulted in the inoperation of mining activities in the area. This research was conducted on the slopes of the Quarry C mine which had experienced a landslide. This study aims to determine the causes of landslides that occur, determine the value of cohesion, deep friction angles and safety factors when landslides occur, and recommend safe slope geometry with the input parameters results of back analysis. In this study, to determine the type of avalanche that occurs is done with stereographic projections that refer to the criteria of the landslide Hoek and Bray, 1981. Data taken in the form of strike and discontinuous dip fields using a geological compass. The initial parameter input uses physical property test data to obtain the value of natural density and mechanical properties testing, namely the shear strength test to obtain the value of cohesion and deep friction angle, as well as the compressive strength test to get the modulus young and poisson ratio values. To find out the value of cohesion, the friction angle in the safety factor during a landslide is performed back analysis using the probability method. Based on the results of data processing and data analysis conducted, it can be concluded that the landslides that occurred in section C1 to section C3 were in the form of arc slides. The results of back analysis of landslides in sections C1 through section C3 are in the form of cohesion and friction angle during landslides, namely for claystone lithology (c = 129.3 kPa, Ø = 25.04o) and for Marly Limestone lithology (c = 80.17 kPa, Ø = 11.23o). For the recommended slope geometry in section C1 is α = 8 o, H = 37.265 m with FK = 1,299 and section C2 is α = 10 o, H = 44.712 m with FK = 1,313. Abstrak. PT X adalah salah satu produsen semen yang mempunyai tambang batugamping di Kecamatan Palimanan, Kabupaten Cirebon, Provinsi Jawa Barat. Pada area penambangan batugamping Kuari C telah terjadi longsoran yang mengakibatkan tidak bisa beroperasinya kegiatan penambangan di area tersebut. Penelitian ini bertujuan untuk mengetahui penyebab kelongsoran yang terjadi, mengetahui nilai kohesi, sudut gesek dalam dan faktor keamanan saat terjadi longsor, serta merekomendasikan geometri lereng yang aman dengan input parameter hasil analisis balik. Pada penelitian ini, untuk mengetahui jenis longsoran yang terjadi dilakukan dengan proyeksi stereografi yang mengacu pada kriteria longsoran Hoek and Bray, 1981. Data yang diambil berupa strike dan dip bidang diskontinu menggunakan kompas geologi. Input parameter awal menggunakan data hasil pengujian sifat fisik untuk mendapatkan nilai natural density dan pengujian sifat mekanik yaitu uji kuat geser untuk mendapatkan nilai kohesi dan sudut gesek dalam, serta uji kuat tekan untuk mendapatkan nilai modulus young dan poisson ratio. Untuk mengetahui nilai kohesi, sudut gesek dalam faktor keamanan saat terjadi longsor dilakukan analisis balik dengan metode probabilitas. Berdasarkan hasil pengolahan data dan analisis data yang dilakukan, dapat disimpulkan bahwa longsoran yang terjadi pada section C1 sampai dengan section C3 berupa longsoran busur. Hasil analisis balik kelongsoran di section C1 sampai dengan section C3 berupa nilai kohesi dan sudut gesek dalam saat terjadi longsor, yaitu untuk litologi claystone (c = 129.3 kPa, Ø = 25.04o) dan untuk litologi Marly Limestone (c = 80.17 kPa, Ø = 11.23o). Untuk geometri lereng yang direkomendasikan pada section C1 adalah α = 8 o, H = 37.265 m dengan FK = 1,299 dan section C2 adalah α = 10 o, H = 44.712 m dengan FK = 1,313.

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be4B8 isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer’s probability of occurrence in a Boltzmann-weighted superposition of each isomer’s spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer–enantiomer and enantiomer–achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.