How Large Fraction of A Population Must be Vaccinated before A Disease is Controlled?

The ongoing Covid-19 pandemic has already caused more than 5 million casualties despite hard restrictions and relatively high vaccine coverage in many countries. The crucial question is therefore, how large vaccination rate and how severe restrictions are required to terminate the spread of the decease, assuming that the vaccine efficiency and the basic reproduction ratio (R0) are known? To answer this question, a mathematical equation was applied to visualize the required vaccination level as function of vaccine efficiency, restriction efficiency and basic reproduction ratio (R0). In addition to the modelling study, Covid-19 data from Europe was collected during 19/11-26/11 (2021) to assess the relation between vaccination rate and incidence. The analysis indicates that a vaccination rate of ~92% (2 doses) is required to stop Delta (B.1.617.2) without severe restrictions, under conditions like those in Europe late November 2021. A third vaccine dose, improved vaccines, higher vaccination rates and/or stronger restrictions will be required to force Omicron (B.1.1.529) to expire without infecting a large fraction of the population.

How Large Fraction of A Population Must be Vaccinated before A Disease is Controlled?

The ongoing Covid-19 pandemic has already caused more than 5 million casualties despite hard restrictions and relatively high vaccine coverage in many countries. The crucial question is therefore, how large vaccination rate and how severe restrictions are required to terminate the spread of the decease, assuming that the vaccine efficiency and the basic reproduction ratio (R0) are known? To answer this question, a simple mathematical equation was developed to visualize the required vaccination level as function of vaccine efficiency, restriction efficiency and basic reproduction ratio (R0). In addition to the modelling study, Covid-19 data from Europe was collected during 19/11-26/11 (2021) to assess the relation between vaccination rate and incidence. The analysis indicates that a vaccination rate of ~92% (2 doses) is currently required to stop Delta (B.1.617.2) without severe restrictions, using the vaccines that are most common in Europe today. A third vaccine dose, improved vaccines, higher vaccination rates and/or stronger restrictions will be required to force Omicron (B.1.1.529) to expire without infecting a large fraction of the population.

A Power Demand Analytical Model of Self-Propelled Vessels

The article herein presents a closed-form mathematical equation by which it is possible to estimate the propulsion power demand of ships as a function of the propeller parameters and total Resistance. The validation of the derived model is conducted by use of the Series 60 Model data and of the Korea Research Institute of Ships and Ocean Engineering (KRISO) Very Large Crude-oil Carrier 2 (KVLCC2) data. In all the cases tested, the derived model explained more than 99.9% of the data variability. Furthermore, the paper describes a practical method for quantifying changes in hull and propeller performance and provides an application example.

Impact of 2nd Wave of COVID-19 Related Lockdown on Coastal Water Quality at Diu, Western Coast of India and Role of Total Alkalinity on Bacterial Loads

A detailed coastal water monitoring near Diu coast, western part of India was performed from October, 2020 to May, 2021 covering the 2nd lockdown time. Average monthly fluctuation from 7 different sampling stations of total 9 physico-chemical parameters such as pH, salinity, turbidity, nitrite (NO2), nitrate (NO3), ammonia (NH3), phosphate (PO4), total alkalinity and silicate were recorded. Initially, Mann-Kendall trend test for all the 9 parameters showed non-zero trend, which may be either linear or non-linear. During 2nd lockdown period, there was a fluctuation of value for parameters like pH, salinity, nitrate, nitrite and phosphate. Average total bacterial count and differential bacterial count also gradually decreased from March, 2021 sampling. Principal component analysis (PCA) plot covering all the physico-chemical parameters as well as the differential bacterial count showed a distinct cluster of all bacterial count with total alkalinity value. Subsequently, mathematical equation was formulated between total alkalinity value and all differential bacterial count. Upto our knowledge this is the first report where mathematical equation was formulated to obtain value of different bacterial load based on the derived total alkalinity value of the coastal water samples near Diu, India.

Prediction the Performance Rate of Chain Type Trenching Machine

The mathematical analysis for estimating the performance rate "RP" of chain-type trenching machine was studied. The mathematical analysis ended with an equation for this type. This mathematical equation was checked under different operating conditions. The practical study of the performance rate showed that the deviation of the theoretical performance rate from the actual performance rate ranged from -3.4 to +2% only for the 150.7 cm and 120.7 cm trench depth respectively. The machine field efficiency ranged from 46.7 to 57% for the 150.7 cm and 120.7 cm depth respectively. It also showed an increase in machine field efficiency by decreasing the trench depth.

My mind is not the universe – where/what is the universe?

In order to describe my findings/conclusions systematically, a new semantic system (i.e., a new language) has to be intentionally defined by the present article. Humans are limited in what they know by the technical limitation of their cortical language network. The conventionally-called “physical/objective reality” around my conventionally-called “physical/objective body” is actually a geometric mathematical model (being generated/mathematically-modeled by my brain) – it's actually a subset/component/part/element of my brain’s mind/consciousness. A reality is a situation model (SM). Our universe is an autonomous objective parallel computing automaton (aka state machine) which evolves by itself automatically/unintentionally – wave-particle duality and Heisenberg’s uncertainty principle can be explained under this SM of my brain. Each elementary particle (as a building block of our universe) is an autonomous mathematical entity itself (i.e., a thing in itself). Our universe has the same nature as a Game of Life system – both are autonomous objective parallel-computing automata. If we are happy to accept randomness, then it is obviously possible that all other worlds in the many-worlds interpretation do not exist objectively. The conventionally-called “space” does not exist objectively. “Time” and “matter” are not physical. Consciousness is the subjective-form (aka quale) of the mathematical models (of the objective universe) which are intracorporeally/subjectively used by the control logic of a Turing machine’s program directly-fatedly. A Turing machine’s consciousness or deliberate decisions/choices should not be able to actually/objectively change/control/drive the (autonomous or directly-fated) worldline of any elementary particle within this world. Besides the Schrodinger equation (or another mathematical equation/function which is yet to be discovered) which is a valid/correct/factual causality of our universe, every other causality (of our universe) is either invalid/incorrect/counterfactual or can be proved by deductive inference based on the Schrodinger equation (or the aforementioned yet-to-be-discovered mathematical equation/function) only. Consciousness plays no causal role (“epiphenomenalism”), or in other words, any cognitive/behavioural activity can in principle be carried out without consciousness (“conscious inessentialism”). If the “loop quantum gravity” theory is correct, then time/space does not actually/objectively exist in the objective-evolution of the objective universe, or in other words, we should not use the subjective/mental concept of “time”, “state” or “space” to describe/imagine the objective-evolution of our universe.

My mind is not the universe – where/what is the universe?

In order to describe my findings/conclusions systematically, a new semantic system (i.e., a new language) has to be intentionally defined by the present article. Humans are limited in what they know by the technical limitation of their cortical language network. The conventionally-called “physical/objective reality” around my conventionally-called “physical/objective body” is actually a geometric mathematical model (being generated/mathematically-modeled by my brain) – it's actually a subset/component/part/element of my brain’s mind/consciousness. A reality is a situation model (SM). Our universe is an autonomous objective parallel computing automaton (aka state machine) which evolves by itself automatically/unintentionally – wave-particle duality and Heisenberg’s uncertainty principle can be explained under this SM of my brain. Each elementary particle (as a building block of our universe) is an autonomous mathematical entity itself (i.e., a thing in itself). Our universe has the same nature as a Game of Life system – both are autonomous objective parallel-computing automata. If we are happy to accept randomness, then it is obviously possible that all other worlds in the many-worlds interpretation do not exist objectively. The conventionally-called “space” does not exist objectively. “Time” and “matter” are not physical. Consciousness is the subjective-form (aka quale) of the mathematical models (of the objective universe) which are intracorporeally/subjectively used by the control logic of a Turing machine’s program directly-fatedly. A Turing machine’s consciousness or deliberate decisions/choices should not be able to actually/objectively change/control/drive the (autonomous or directly-fated) worldline of any elementary particle within this world. Besides the Schrodinger equation (or another mathematical equation/function which is yet to be discovered) which is a valid/correct/factual causality of our universe, every other causality (of our universe) is either invalid/incorrect/counterfactual or can be proved by deductive inference based on the Schrodinger equation (or the aforementioned yet-to-be-discovered mathematical equation/function) only. Consciousness plays no causal role (“epiphenomenalism”), or in other words, any cognitive/behavioural activity can in principle be carried out without consciousness (“conscious inessentialism”). If the “loop quantum gravity” theory is correct, then time/space does not actually/objectively exist in the objective-evolution of the objective universe, or in other words, we should not use the subjective/mental concept of “time”, “state” or “space” to describe/imagine the objective-evolution of our universe.

Mathematical modelling of crushed rock dust concrete: Performance using compressive strength

The paper gives out a mathematical model developed using linear regression statistical method to envisage the 28-day strength of CRD concrete, considering M20, M30 and M40 grades concrete and CRD replacement percentages of 0%, 10%, 20%, 30% and 40% by weight of cement. Strength results of M40, M30 and M20 grades concrete are used to develop the relationship between CRD content and compressive strength. The ratios of compressive strengths between CRD and control concrete (CC) have been related to CRD replacement percentage. The expression, derived is with strength ratios and not with experimental strength values. The mathematical equation developed is independent of the specimen parameters and may be applicable to all types of specimens. The model is considered as it involves non-dimensional variables and is independent of the specimen size, water to binder ratio (w/b) and grade of concrete.

Using 6 questions cognitive method and polya’s model to helps students solve mathematical problem

The ability to solve the mathematical equation problem is very important for the thinking development of middle school students. “How to solve it” of George Polya is famous in the world. 6 questions cognitive model proposed by Professor Zhou are monitored through metacognition, and the 6 questions are coherent, complete and sequential. This paper found that the 6 questions cognitive model can help implement “How to solve it” of George Polya and reduce students' cognitive load. At the same time, this study found that 6 questions cognitive model can help students solve the mathematical equation problem better.