Analysis of Sales Predictions from the Point of View of the Increase in Daily Newspaper Sales

This study aims at Analysis of Sales Predictions from the Point of View of the Increase in Daily Newspaper Sales. The methods of this research is gather evidence through a variety of approaches, including library analysis and field research. This paper makes use of both qualitative and quantitative evidence. Primary data sources, namely data collected from respondents or direct interviews with business executives, specifically about marketing strategies, especially those relating to promotion. Secondary evidence.  Promotional operations are carried out optimally, which is facilitated by sufficient costs, especially in potential areas. Apart from repeat buyers, the organization offers its goods in store, which enables the company to monitor its output figures accurately and seamlessly.

New Results in the Artin Approximation Theory and the Construction of General Neron Desingularization

If everyfinitesystemofpolynomialequationsoveraring R has asolutioninthe ring R if andonlyifithasasolutionin ˆR where ˆR representsthecompletionof R, then wesaythatthering R has the Artinapproximationproperty. M.Artinsetin a numberofconjectures,thefollowingtheoremsolvedoneofthemwhichsays,“an excellentHenselianlocalringhasthepropertyofArtinapproximation”.General Neron Desingularizationisthebaseoftheproof. Let R and R0 beNoetherianrings,foraspecial(thatisregular)morphism u : R ! R0, any R-morphism '' : S ! R0 with afinitetype R-algebra S, factors through an R-algebra T whichissmooth R-algebra, thatis, '' is acomposite Rmorphism of S ! T and T ! R0. The R-algebra T is calledaGeneralN´eron Desingularization (shortlyGND). In ourthesiswegivetheconstructiveproofofGeneralNeronDesingularization for thecasewhen R and R0 are localringsofdimension m and S has abigsmooth locus,wealsogiveauniformGeneralNeronDesingularizationforlocalringsofdi- mension m along withthealgorithmstoconstructtheN´eronDesingularizationin these cases.Anothercontributionisthat,wegivethenestedstrongArtinapproxi- mation.