Ring Protons Research Articles

Magnetosonic Waves Excited by Maxwellian Ring Protons in Space Plasma Environment

A comprehensive theoretical model for a homogeneous plasma system of hot, tenuous Maxwellian ring-distributed protons and the cold background of Maxwellian ions and electrons is used to study the resonant instabilities of magnetosonic (MS) waves. The perpendicular velocity integrals associated with the Maxwellian ring distribution have no analytical solution, hence, are solved numerically, while the parallel velocity integrals are solved analytically by invoking series expansion of the plasma dispersion function. For the plasma parameters relevant to Earth’s inner magnetosphere, the theoretical model generates MS waves with frequencies from 5 times the local proton cyclotron frequency to above the lower hybrid frequency for a propagation angle of 89.5°. Hydrogen (H+) band electromagnetic ion cyclotron waves are also excited by the Maxwellian ring protons for the same set of plasma parameters. A detailed analysis reveals that a sufficiently large ring velocity, as well as a smaller perpendicular and parallel thermal velocity, can enhance the MS wave growth. The study also explores the role of background plasma parameters in modulating the waves. The present theoretical model reproduces the harmonics of the MS waves observed by the Van Allen Probes in the Earth’s inner magnetosphere. Further, the model can generate MS waves in other plasma environments, e.g., Mars, where the presence of ring protons has been established by MAVEN in connection with the MS wave observations.

Monte Carlo QM/MM simulation studies of the Cannizzaro reaction in ionic liquids for improved biofuel production.

The conversion of biomass to 5-hydroxymethylfurfural (HMF) holds substantial promise as a renewable energy source. Notably, HMF can be transformed into 2,5-bis(hydroxymethyl)furan (BHMF), a crucial reactant in biofuel production, but requires harsh operating conditions, H2, and precious metal catalysts. A recently reported Cannizzaro reaction of HMF to BHMF, characterized by its efficiency, mild conditions, and eco-friendliness, instead employed ionic liquids (ILs) to achieve high yields. In this study, combined quantum mechanical and molecular mechanical (QM/MM) simulations in conjunction with Metropolis Monte Carlo statistical mechanics and free-energy perturbation theory utilized M06-2X/6-31+G(d), PDDG/PM3, and the OPLS-VSIL force field to uncover important solute-solvent interactions present in the HMF to BHMF reaction pathway. The Cannizzaro reaction was examined in water and in five ILs composed of the 1-butyl-3-methylimidazolium [BMIM] cation coupled to hexafluorophosphate, tetrafluoroborate, thiocyanate, chloride, and bromide. Energetic and structural analysis of the rate-determining hydride transfer between HMF and the hydride-donor anion HMFOH- attributed the enhanced reactivity to highly organized solvent interactions featuring (1) hydrogen bonding between the ring protons of [BMIM] and the negatively charged carbonyl oxygen atoms on the transition structure, (2) favorable electrostatic interactions between the IL anions and solute hydroxyl groups, and (3) beneficial π-π stacking interactions between [BMIM] and the two aromatic rings present in HMF and HMFOH-.

Fluoride-Mediated Aryne 1,2-Difunctionalization Involving C═S Bond Heterolysis.

We have successfully synthesized a series of bidentate ligands by utilizing 2-(trimethylsilyl)phenyl trifluorosulfonate as a precursor for the benzyl group. This method proceeded by inserting a polythiourea into the C═S π-bond, intramolecular ring proton migration, and ring opening. Salient features of this strategy are mild reaction conditions, a novel product structure, excellent stereochemistry, and a good functional group tolerance. Furthermore, a series of density functional theory calculations were performed to gain insights into the transfer mechanism.

Fine Structure of Magnetospheric Magnetosonic Waves: 1. Elementary Rising‐Tone Emissions Within Individual Harmonic

AbstractThe present study uncovers the fine structures of magnetosonic waves by investigating the EFW waveforms measured by Van Allen Probes. We show that each harmonic of the magnetosonic wave may consist of a series of elementary rising‐tone emissions, implying a nonlinear mechanism for the wave generation. By investigating an elementary rising‐tone magnetosonic wave that spans a wide frequency range, we show that the frequency sweep rate is likely proportional to the wave frequency. We studied compound rising‐tone magnetosonic waves, and found that they typically consist of multiple harmonics in the source region, and may gradually become continuous in frequency as they propagate away from source. Both elementary and compound rising‐tone magnetosonic waves last for ∼1 min which is close to the bounce period of the ring proton distribution, but their relation is not fully understood.

Synthesis and characterization of carbonyl functionalized organotellurium(iv) derivatives.

The current study focuses on synthesis and characterization of carbonyl functionalized unsymmetrical diorganotellurium(iv) dichlorides (1-5), dibromide (6), and their characterization by elemental analysis, 1H, 13C{1H}, and 125Te NMR spectroscopy. In addition to this, compounds 1, 4 and 5 were further confirmed via single-crystal X-ray studies. Reduction of all the dichlorides with Na2S2O5 affords labile tellurides, which decompose quickly even at room temperature into the more stable symmetric ditellurides, Ar2Te2. Mesityl fragments bearing organotellurium(iv) derivatives show separate 1H and 13C{1H} NMR signals for the ortho methyls and meta protons of the mesityl ring. Among the Te(iv) dichlorides, the observed O-H⋯O, C-H⋯O, C-H⋯Cl, Te⋯O and Te⋯Cl hydrogen and secondary bonding interactions are longer than Σr cov (sum of the covalent bond radii) and significantly shorter than Σr vdw (sum of the van der Waal radii) respectively. The linearity of the C-Te⋯O, C-H⋯O and C-H⋯Cl makes n → σ* orbital interaction possible.

SYNTHESIS, CHARACTERIZATION, AND ANTIMICROBIAL EVALUATION OF IMINE-LINKED BENZOTHIAZINE COMPOUNDS BY ULTRASOUND METHOD

This work seeks to evaluate the antibacterial properties of the compounds and create imine-linked benzothiazine derivatives using a novel, eco-friendly ultrasonic technique. Escherichia coli and Staphylococcus aureus were utilized to assess the synthetic compounds, SBIa-e, for their antibacterial activity. All compounds were soluble in organic solvents but insoluble in water, with yields ranging from 68 to 77%. The molecules showed stretching vibrations corresponding to various functional groups. The presence of amine hydrogen (2.0, 7.0 ppm), aliphatic protons (2.6- 4.3 ppm), imine hydrogen (8.0-8.5 ppm), and protons of the aromatic ring (6.8-7.9 ppm) was indicated by the 1HNMR spectra. Both the bacterial strains were all susceptible to the antibacterial action of the compounds, which showed dose-dependent effects. When the compounds were compared to gram-positive bacteria, it was discovered that the former had greater effectiveness than the latter. SBId had the lowest IC50 against Staphylococcus aureus (70.16 µg/mL) and Escherichia coli (49.19 µg/mL) among the drugs whose IC50 values were calculated.

Синтез и исследование структуры иодсодержащих имидазо[2,1 b][1,3]тиазиниевых систем

Heterocyclization of S-alkenyl derivatives of 1-methylimidazole-2-thiol (1-methyl-2-prenyl-sulfanylimidazole (1), 1-methyl-2-cinnamylsulfanylimidazole (4), and 2-(3-butenyl)sulfanyl-1-methyl-imidazole (7)) has been studied for the first time under the action of iodine (iodocyclization) in various solvents (chloroform, dichloro-methane, glacial acetic acid), and at different substrate and iodine ratios (1 : 1, 1 : 2). It has been found that the interaction of compounds 1, 4, 7 with iodine proceeds regioselectively, regardless of the reaction conditions, and it is accompanied by the linear annelation of the thiazinium ring and formation of a bicyclic fused heterocyclic system. As a result, new iodine-containing imidazo[2,1 b][1,3]thiazinium systems have been synthesized – 6-iodo-1,5,5-trimethyl-6,7-dihydro-5H-imidazo[2,1-b][1,3]hiazinium polyiodide / iodide (2, 3), 6-iodo-1-methyl-5-phenyl-6,7-dihydro-5H-imidazo[2,1-b][1,3]thiazinium triiodide / iodide (5, 6), and 6-iodomethyl-1-methyl-6,7-dihydro-5H-imidazo[2,1-b][1,3]thiazinium iodide (9). The structure of the synthesized compounds has been studied and proved by 1H and 13C NMR spectroscopy. The evidence for heterocyclization reactions of alkenyl sulfides 1, 4, and 7 is the absence of signals for the alkenyl protons and the presence of a more complex splitting pattern of signals for the thiazinium ring protons in the 1H NMR spectra of heterocyclization products. The structures of polyiodide 2 and triiodide 5 have been unambiguously established and characterized by X-ray diffraction analysis. According to the X-ray analysis data, the cell of polyiodide 2 contains two heterocyclic cations, a triiodide anion, and an iodide anion. In the triiodide crystal 5 heterocyclic cations correspond to two types of crystallographically independent triiodide anions: one cell contains eight molecules of a heterocyclic cation and eight triiodide anions. The structural organization in the crystals is due to short contacts between atoms: I(4)∙∙∙H(3) (2.95 Å), I(4)∙∙∙I(1) (3.57 Å), H(8a)∙∙∙I(2) (3.13 Å) (in crystal 2), I(2)∙∙∙I(4) (3.95 Å), I(5)∙∙∙H(5) (3.14 Å), I(4)∙∙∙H(7a) (3.12 Å), I(4)∙∙∙H(7b) (3.17 Å) (in crystal 5).

Quantum Mechanical/Molecular Mechanical Elucidation of the Catalytic Mechanism of Leukotriene A4 Hydrolase as an Epoxidase.

Leukotriene A4 hydrolase (LTA4H) functions as a mono-zinc bifunctional enzyme with aminopeptidase and epoxidase activities. While the aminopeptidase mechanism is well understood, the epoxidase mechanism remains less clear. In continuation of our prior research, we undertook an in-depth exploration of the LTA4H catalytic role as an epoxidase, employing a combined SCC-DFTB/CHARMM method. In the current work, we found that the conversion of LTA4 to leukotriene B4 (LTB4) involves three successive steps: epoxy ring opening (RO), nucleophilic attack (NA), and proton transfer (PT) reactions at the epoxy oxygen atom. Among these steps, the RO and NA stages constitute the potential rate-limiting step within the entire epoxidase mechanism. Notably, the NA step implicates D375 as the general base catalyst, while the PT step engages protonated E271 as the general acid catalyst. Additionally, we delved into the mechanism behind the formation of the isomer product, Δ6-trans-Δ8-cis-LTB4. Our findings debunked the feasibility of a direct LTB4 to iso-LTB4 conversion. Instead, we highlight the possibility of isomerization from LTA4 to its isomeric conjugate (iso-LTA4), showing comparable energy barriers of 5.1 and 5.5 kcal/mol in aqueous and enzymatic environments, respectively. The ensuing dynamics of iso-LTA4 hydrolysis subsequently yield iso-LTB4 via a mechanism akin to LTA4 hydrolysis, albeit with a heightened barrier. Our computations firmly support the notion that substrate isomerization exclusively takes place prior to or during the initial substrate-binding phase, while LTA4 remains the dominant conformer. Notably, our simulations suggest that irrespective of the active site's constrained L-shape, isomerization from LTA4 to its isomeric conjugate remains plausible. The mechanistic insights garnered from our simulations furnish a valuable understanding of LTA4H's role as an epoxidase, thereby facilitating potential advancements in inhibitor design.

Cholapod and Cholaphanes for Recognition of Anions

abstract: Deoxycholic and cholic acid-based receptors 6, 13, and 16 containing imidazolium groups were synthesized, and their properties as anion receptors have been evaluated. Cholaphanes 13 and 16 exhibited moderate binding selectivity and affinity for fluoride ions, while cholapod 6 showed low binding selectivity and affinity for chloride ions due to the presence of a nitro group in the imidazolium ring. The H-bonding interactions involve C-2 protons of imidazolium ring with anion. The detection of halide ions is revealed by the binding constant through the 1H NMR titration experiment.

Unveiling the complexation mechanism of phloretin with Sulfobutylether–β–cyclodextrin (Captisol®) and its impact on anticancer activity

The incorporation of phloretin (PHL), a dihydrochalcone flavonoid, in functional foods is usually hampered by its low aqueous solubility. In this regard, we investigated the impact of complexation of PHL with sulfobutylether-β-cyclodextrin (SBE-β-CD, Captisol®) to overcome its limitation. The phase solubility studies of PHL with different β-CDs derivatives represents AL-type of curve where, SBE-β-CD demonstrated highest apparent stability constant (Ks: 15,856 M−1) indicating its strong affinity to form host-guest assembly. Solid-state characterizations (including SEM, FT-IR, PXRD, DSC, TGA) provided direct evidences of inclusion complex (IC) formation. The detailed molecular interaction between the host–guest assembly was performed using 1H NMR and 2D-NOESY revealed that protons of aromatic phenyl ring of PHL (guest) molecule exhibit direct correlation with the protons lying in the inner cavity of SBE-β-CD (host). Furthermore, the anticancer potential of PHL/SBE-β-CD-IC was examined using cytotoxicity studies, caspase 3/7 activation assay, reactive oxygen species (ROS) generation and disturbance in mitochondrial membrane potential (MMP) in lung carcinoma cell line (A549) and human pancreatic cancer cell line (MiaPaCa–2). The in-vitro cytotoxicity assay on both cell lines demonstrated higher antiproliferative activity of IC as compared to free PHL in concentration dependent manner. In addition, it was found that PHL/SBE-β-CD-IC induces apoptosis via activation of caspase 3/7, reactive oxygen species generation and inducing depolarization of mitochondrial membrane potential in both the cell lines (MiaPaCa–2 and A549). Overall, the study provides a promising approach to enhance the solubility and bioactivity of PHL utilizing SBE-β-CD inclusion complexation.

Quantum chemical study of the acidity оf 3,4-dihydro-2Н-thiopyran-1,1-dioxides

We conducted quantum chemical modelling by REVPBE0 3,4-dihydro-2H-thiopyran-1,1-dioxide,3,4,6-triphenyl-3,4-dihydro-2H-thiopyran-1,1-dioxide and their anions. The authors calculated the Gibbs free energies for the reaction of their interaction with hydroxide anion as a base. We have found a difference in the acidic properties of the protons of the 2H-thiopyran rings and the positions of the reaction centres in the subsequent reactions involving the formed anions.

Molecular Architecture Effects on Bulk Nanostructure in Bis(Orthoborate) Ionic Liquids.

A series of 19 ionic liquids (ILs) based on phosphonium and imidazolium cations of varying alkyl-chain lengths with the orthoborate anions bis(oxalato)borate [BOB]- , bis(mandelato)borate, [BMB]- and bis(salicylato)borate, [BScB]- , are synthesized and studied using small-angle neutron scattering (SANS). All measured systems display nanostructuring, with 1-methyl-3-n-alkyl imidazolium-orthoborates forming clearly bicontinuous L3 spongelike phases when the alkyl chains are longer than C6 (hexyl). L3 phases are fitted using the Teubner and Strey model, and diffusely-nanostructured systems are primarily fitted using the Ornstein-Zernicke correlation length model. Strongly-nanostructured systems have a strong dependence on the cation, with molecular architecture variation explored to determine the driving forces for self-assembly. The ability to form well-defined complex phases is effectively extinguished in several ways: methylation of the most acidic imidazolium ring proton, replacing the imidazolium 3-methyl group with a longer hydrocarbon chain, substitution of [BOB]- by [BMB]- , or exchanging the imidazolium for phosphonium systems, irrespective of phosphonium architecture. The results suggest there is only a small window of opportunity, in terms of molecular amphiphilicity and cation:anion volume matching, for the formation of stable extensive bicontinuous domains in pure bulk orthoborate-based ILs. Particularly important for self-assembly processes appear to be the ability to form H-bonding networks, which offer additional versatility in imidazolium systems.

Targeted Central Nervous System Irradiation with Proton Microbeam Induces Mitochondrial Changes in Caenorhabditis elegans.

Fifty percent of all patients with cancer worldwide require radiotherapy. In the case of brain tumors, despite the improvement in the precision of radiation delivery with proton therapy, studies have shown structural and functional changes in the brains of treated patients with protons. The molecular pathways involved in generating these effects are not completely understood. In this context, we analyzed the impact of proton exposure in the central nervous system area of Caenorhabditis elegans with a focus on mitochondrial function, which is potentially implicated in the occurrence of radiation-induced damage. To achieve this objective, the nematode C. elegans were micro-irradiated with 220 Gy of protons (4 MeV) in the nerve ring (head region) using the proton microbeam, MIRCOM. Our results show that protons induce mitochondrial dysfunction, characterized by an immediate dose-dependent loss of the mitochondrial membrane potential (ΔΨm) associated with oxidative stress 24 h after irradiation, which is itself characterized by the induction of the antioxidant proteins in the targeted region, observed using SOD-1::GFP and SOD-3::GFP strains. Moreover, we demonstrated a two-fold increase in the mtDNA copy number in the targeted region 24 h after irradiation. In addition, using the GFP::LGG-1 strain, an induction of autophagy in the irradiated region was observed 6 h following the irradiation, which is associated with the up-regulation of the gene expression of pink-1 (PTEN-induced kinase) and pdr-1 (C. elegans parkin homolog). Furthermore, our data showed that micro-irradiation of the nerve ring region did not impact the whole-body oxygen consumption 24 h following the irradiation. These results indicate a global mitochondrial dysfunction in the irradiated region following proton exposure. This provides a better understanding of the molecular pathways involved in radiation-induced side effects and may help in finding new therapies.

CO2-Assisted in situ hydrogen extraction for highly selective aromatization of n-Hexane over Zn modified HZSM-5 catalyst

Controlling the evolution of H species in CO2-assisted alkane activation represents an opportunity for simultaneously upgrading light alkanes and greenhouse gas CO2. Herein, we successfully realized the highly selective aromatization of n-hexane by the assistance of CO2 over Zn modified HZSM-5 catalyst. Multi-characterizations demonstrated that the introduction of CO2 could timely remove the in situ H originated from the C-H activation of n-hexane and cyclohexane through the dynamic evolution of the pentagonal coordination Zn-OH+-(CO)-O-Zn structure. On this basis, hydrogen transfer between olefins and aromatics is effectively inhibited, and the binding between π electrons of benzene ring and hydrogen proton is weakened, accelerating the generation and desorption of BTEX. Therefore, the Zn/ZSM-5-CO2 displays a record high 49.7% BTEX yield, which is nearly 10% higher than that of the Zn/ZSM-5-N2 (40.3%). In addition, the loss of medium strength Lewis acid caused by in situ H reduction of Si(Al)-O-Zn structure is significantly reduced, ensuring its superior catalytic stability under long-term conditions. These results may provide some insights for the profitable utilization of petrochemical resources to aromatics over zeolites.

Synthesis, separation, and characterization of spiro-fused cycloalkyl-embedded 5,15-porphodimethenes

The synthesis of cycloalkyl-fused porphodimethenes from a mixture of products was investigated. Each product was separated via silica gel column chromatography and characterized using nuclear magnetic resonance (NMR) and UV-visible absorption spectroscopies, and mass spectrometry. X-ray crystal structure analysis revealed their gable-like bent conformations bearing perpendicular cycloalkyl rings in which the dipyrrin pairs contacted closely so that the neighboring pyrrole rings formed circular hydrogen bonding networks, such as those in porphyrins. Such configurations also caused extreme downfield shifts of the methylene protons of the cycloalkyl rings in the 1H NMR spectra.

SYMMETRICAL SYNTHESIS AND CHARACTERIZATION OF FIVE-COORDINATE In(III) PORPHYRINS WITH SALICYLIC ACID DERIVATIVES

Investigations of the In(III)porphyrin complexes with substituted salicylates(X) as axial ligands have been carried out using electronic and biological studies. Electronic spectra of the complexes are accompanied by shifting of wavelength towards hypsochromic/blue-shift or bathochromic/red-shift along with 'ƒ' values decided by the nature of the functional groups attached to the salicylate ligand. IR frequencies appear at 550cm-1–400cm−1 for In–N(Por) and at 650cm−1–700cm−1 for In–OSA. 1HNMR spectra reveal the merging of the salicylate ring with that of the protons of the macrocyclic ring. The 13CNMR studies confirm the resonance of the meso-carbon tetraphenyl porphyrin ring between 130ppm to 160ppm and the salicylate ring carbons in the region of 110ppm to 165ppm. Thermal analysis confirms the presence of indium nitride (In-N) in an argon atmosphere from 0oC to 900oC. Cyclic voltammetry(CV) revealed the reduced or oxidized properties of these complexes lead to the generation of π-anion or cation radicals by two one-electron transfer reactions. In(III)porphyrin complexes with substituted salicylates were also screened for in-vitro antifungal activity(%inhibition) against the microbe "Acremonium fusidoides spp." using the PDA method, which shows that the percentage inhibition is inverse to the diameter of the colony. The freeradical scavenging or antiradical activity (%RSA) by the DPPH method reveals that these complexes were absorbance and concentration-dependent.

Growth of pyridinecarbothioamides and single crystal XRD studies

A series of pyridinecarbothioamides (PCT) are synthesized to produce parrot green crystals. The crystal structure of the compounds was resolved using single crystal XRD technique. It confirmed the formation of monoclinic system with different space groups depending on the position of side chains in the carbothioamide. The 3D structural arrangements show that molecules in the crystal structure are interlinked by NH … N or SH … S hydrogen bonding. The conversion of pyridinecarbonitrles to their corresponding pyridinecarbothioamides by the treatment of ammonia and H2S was confirmed by their mass spectra. Major peak was observed at m/z of 138. Thermogram of PCTs, shows a single step decomposition thereby confirming the melting points of corresponding PCT’s as 137 °C, 190 °C, 209 °C respectively. Nuclear Magnetic Resonance (NMR) spectroscopic techniques showed the signals corresponding to pyridine ring protons and amino group.

Dielectric ordering of water molecules in the dipole lattice of potassium hexacyanoferrate(II) trihydrate

The structure of potassium hexacyanoferrate(II) trihydrate (yellow prussiate) contains layers of water molecules between the layers of potassium and ferrocyanide octahedra. When the temperature drops down to 120 K, the water molecules have a tendency to rearrange. The movement of protons in molecular and individual rings occurs in a coordinated manner. The asymmetry of the ring environment leads to a significant decrease of the double-well potential barrier. The theory of coherent correlated motions of protons allows to explain the discreteness of the observed temperature anomalies of dielectric permittivity ε, thermally stimulated depolarization current j, and pyroelectric coefficient γ.

ДРЕЙФОВЫЕ ЭФФЕКТЫ ГЕОМАГНИТНЫХ ПУЛЬСАЦИЙ УЛЬТРАНИЗКОЧАСТНОГО ДИАПАЗОНА

Previously, when analyzing ULF variations of the natural electromagnetic fi according to observations in the Borok and Mondy observatories, separated by 60 degrees of longitude, longitudinal effects of geomagnetic Pc1 pulsations («pearls») were revealed. The effects were manifested themselves as a delay or advance of the beginning of the coherent Pc1 series in Borok in relation to their observation at the Mondy observatory. In 63% and 37% of cases, pulsations in Borok began later and before their detection at the Mondy observatory, respectively. The delay-advance time varied in the range from few minutes to one hour. A hypothesis is proposed about the nature of the revealed phenomenon, which directly associates these longitudinal effects with the drift motion of ring current particles, protons and antiprotons, as the source of pulsations, in the western and eastern direction, respectively. Examples illustrating the revealed effects are given. The assumption is qualitatively and quantitatively assessed.

A comparative analysis of powder ENDOR spectra of aromatic and aliphatic radicals by exact and 1st order simulation

Exact and perturbation methods were employed in simulations of powder ENDOR spectra to obtain the anisotropic hyperfine ( hfc ) and nuclear quadrupole ( nqc ) coupling constants of certain organic radicals of interest in fundamental research and in applications in radiation research, surface chemistry and biophysics. The principal hfc values of the ring protons and methyl substituents for several aromatic cations trapped in disordered matrices might be more accurate than those previously reported using regular EPR. Only one of the earlier assignments of the naphthalene cation spectrum was in acceptable agreement with the simulations. The proton couplings at the β-position of alkyl radicals were deduced by simulations while the spectrum due to α-couplings with appreciable anisotropy was weak. Accurate simulation of the 14 N (I = 1) spectra in bio-radicals was obtained by adjustment of the relative orientation of the principal hfc and nuclear quadrupole coupling ( nqc ) tensors as well as the principal values. Adjustment of the excitation width parameter employed in the software was also required in a few cases to improve the agreement with the experimental spectra. The hfc patterns due to matrix nuclei ( 1 H and 7 Li) around the radicals of X-irradiated samples were simulated to elucidate the nature of the trapping sites in materials used for EPR dosimetry. ENDOR simulation programs known to us are presented in an Appendix. The performance of the ENDORF2 program used in previous works was examined by comparison with exact treatment. Input and output examples, source and executable codes used in this work can be downloaded at https://github.com/EndorF2/Simulation .