Banknotes ad golden guarantee

In this paper, we explain that paper money is a means of collecting government taxes and creating a budget, and since companies and individuals pay taxes on their labor income, they use it to buy labor, goods, and services. A large percentage of taxes are levied on the salaries and profits of individuals and companies, which always leads to a shortage of money. Therefore, most of the population is made up of poor and low-income citizens. Since paper money has no value, merchants raise the prices of goods and commodities for super profits, and by increasing the value of paper money, they stimulate today’s inflation and open a great opportunity for the government to pay off its debts.Another problem is that the US dollar becomes an international reserve currency that is used to control one country’s international trade, to devalue some countries’ national currencies and thus to pressure and destroy their economies. Цаасан мөнгө ба алтан баталгаа ХураангуйБид энэхүү өгүүллээрээ цаасан мөнгө бол засгийн татвар хурааж төсвөө бүрдүүлэх хэрэгсэл байдаг ба аж ахуйн нэгж, хувь хүмүүс хөдөлмөрөөрөө олсон орлогоосоо татвар төлдөг учраас түүнийг хөдөлмөр хийгээд бараа, үйлчилгээ худалдан авахдаа хэрэглэсээр ирсэн түүхтэй. Хувь хүн, компанийн хөдөлмөрийн хөлс, ашиг орлогоос ихээхн хувь хэмжээтэй татвар авдаг нь тэднийг ямагт мөнгөний гачигдал хомсдолд оруулж байдаг билээ. Тиймээс хүн амын дийлэнх нь ядуу, ядуувтар орлоготой иргэн байдаг. Цаасан мөнгө үнэ цэнгүй учраас бараа, таваарын үнийг худалдаачид хэт ашгийн төлөө асар өсгөдөг бөгөөд ихгэснээр цаасан мөнгө үнэгүйдэж өнөө үеийн инфляц гээчийг өдөөж, засгийн газраас өр төлбөрөө барагдуулах ихээхэн боломж нээж байна.Нөгөө нэг асуудал бол АНУ-ын доллар олон улсын нөөц валют болсноор олон улсын худалдаанд нэг орны хяналт тогтох, зарим орны үндэсний валютын ханшийг унагах, ингэснээр эдийн засгийг нь дарамт, сүйрэлд оруулах хэрэгсэл болгож буйг үүгээр тодорхойлохыг зорив.Tүлхүүр үгс: цаасан мөнгө, алт, баталгаа, геополитик, үндэсний мөнгөн тэмдэг

On Sombor Index of Graphs

Recently, Gutman defined a new vertex-degree-based graph invariant, named the Sombor index $SO$ of a graph $G$, and is defined by $$SO(G)=\sum_{uv\in E(G)}\sqrt{d_G(u)^2+d_G(v)^2},$$ where $d_G(v)$ is the degree of the vertex $v$ of $G$. In this paper, we obtain the sharp lower and upper bounds on $SO(G)$ of a connected graph, and characterize graphs for which these bounds are attained

Reduced Sombor index of bicyclic graphs

The concept of Sombor indices (SO) of a graph was recently introduced by Gutman and the reduced Sombor index [Formula: see text] of a graph [Formula: see text] is defined by [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text]. In this paper, we study the extremal properties of the reduced Sombor index and characterize the bicyclic graphs with extremal [Formula: see text]-value. </jats:p

Linear Regression Based Real-Time Filtering

This paper introduces real time filtering method based on linear least squares fitted line. Method can be used in case that a filtered signal is linear. This constraint narrows a band of potential applications. Advantage over Kalman filter is that it is computationally less expensive. The paper further deals with application of introduced method on filtering data used to evaluate a position of engraved material with respect to engraving machine. The filter was implemented to the CNC engraving machine control system. Experiments showing its performance are included

On Zagreb indices of graphs

Let ${\mathcal G}_n$ be the set of class of graphs of order $n$. The first Zagreb index $M_1(G)$ is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index $M_2(G)$ is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph $G$. The three set of graphs are as follows: \begin{eqnarray*} &&A=\left\{G\in {\mathcal G}_n:\,\frac{M_1(G)}{n}>\frac{M_2(G)}{m}\right\},~B=\left\{G\in {\mathcal G}_n:\,\frac{M_1(G)}{n}=\frac{M_2(G)}{m}\right\} \mbox{ and }&& &&~~~~~~~~~~~~~~~~~~~~~~~~~C=\left\{G\in {\mathcal G}_n:\,\frac{M_1(G)}{n}<\frac{M_2(G)}{m}\right\}. \end{eqnarray*} In this paper we prove that $|A|+|B|<|C|$. Finally, we give a conjecture $|A|<|B|$

Comparing Zagreb indices for connected graphs

AbstractIt was conjectured that for each simple graph G=(V,E) with n=|V(G)| vertices and m=|E(G)| edges, it holds M2(G)/m≥M1(G)/n, where M1 and M2 are the first and second Zagreb indices. Hansen and Vukičević proved that it is true for all chemical graphs and does not hold in general. Also the conjecture was proved for all trees, unicyclic graphs, and all bicyclic graphs except one class. In this paper, we show that for every positive integer k, there exists a connected graph such that m−n=k and the conjecture does not hold. Moreover, by introducing some transformations, we show that M2/(m−1)>M1/n for all bicyclic graphs and it does not hold for general graphs. Using these transformations we give new and shorter proofs of some known results

Cactus Graphs with Maximal Multiplicative Sum Zagreb Index

A connected graph G is said to be a cactus if any two cycles have at most one vertex in common. The multiplicative sum Zagreb index of a graph G is the product of the sum of the degrees of adjacent vertices in G. In this paper, we introduce several graph transformations that are useful tools for the study of the extremal properties of the multiplicative sum Zagreb index. Using these transformations and symmetric structural representations of some cactus graphs, we determine the graphs having maximal multiplicative sum Zagreb index for cactus graphs with the prescribed number of pendant vertices (cut edges). Furthermore, the graphs with maximal multiplicative sum Zagreb index are characterized among all cactus graphs of the given order.</jats:p