Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. Aft...Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. After a finite number of operations, a palindrome number must be obtained. We firstly give out several definitions: The pure-single-digit-of-sum is the number of single digits that only count the sum of two numbers of the same digit in the vertical operation of addition, which is referred to as pure single digit for short, denoted by g. The pure-carry-digit-of-sum is the carry digit that only counts the sum of two numbers in the same bit in the vertical operation of addition. It is a special number composed of only 1 and 0, which is represented by j'. The complement-0-carry-digit-of-sum is to supplement a 0 on the last side of j' according to the rule of adding bits, which is denoted by j. Therefore, in the addition operation, the sum of any natural number and its inverse ordinal number is divided into two parts: g and j. Then, the characteristics of g and j are characterized by the following two theorems: Theorem 1: As all the numbers in j are 0, j is the palindrome number;As the numbers in j are not all 0, j is not a palindrome number. Theorem 2: The sum of any palindrome number H and any non-palindrome j number must be a non-palindrome number. Then we proved the palindrome number conjecture is not correct by using the above two theorems.展开更多
Orphan diseases are rare diseases that affect less than 200000 individuals within the United States.Most orphan diseases are of neurologic and genetic origin.With the current advances in technology,more funding has be...Orphan diseases are rare diseases that affect less than 200000 individuals within the United States.Most orphan diseases are of neurologic and genetic origin.With the current advances in technology,more funding has been devoted to developing therapeutic agents for patients with these conditions.In our review,we highlight emerging options for patients with neurologic orphan diseases,specifically including diseases resulting in muscular deterioration,epilepsy,seizures,neurodegenerative movement disorders,inhibited cognitive development,neuron deterioration,and tumors.After extensive literature review,gene therapy offers a promising route for the treatment of neurologic orphan diseases.The use of clustered regularly interspaced palindromic repeats/Cas9 has demonstrated positive results in experiments investigating its role in several diseases.Additionally,the use of adeno-associated viral vectors has shown improvement in survival,motor function,and developmental milestones,while also demonstrating reversal of sensory ataxia and cardiomyopathy in Friedreich ataxia patients.Antisense oligonucleotides have also been used in some neurologic orphan diseases with positive outcomes.Mammalian target of rapamycin inhibitors are currently being investigated and have reduced abnormal cell growth,proliferation,and angiogenesis.Emerging innovations and the role of genetic treatments open a new window of opportunity for the treatment of neurologic orphan diseases.展开更多
Pancreatic cancer(PC)remains one of the most challenging diseases,with a very poor 5-year overall survival of around 11.5%.Kirsten rat sarcoma virus(KRAS)mutation is seen in 90%-95%of PC patients and plays an importan...Pancreatic cancer(PC)remains one of the most challenging diseases,with a very poor 5-year overall survival of around 11.5%.Kirsten rat sarcoma virus(KRAS)mutation is seen in 90%-95%of PC patients and plays an important role in cancer cell proliferation,differentiation,metabolism,and survival,making it an essential mutation for targeted therapy.Despite extensive efforts in studying this oncogene,there has been little success in finding a drug to target this pathway,labelling it for decades as“undruggable”.In this article we summarize some of the efforts made to target the KRAS pathway in PC,discuss the challenges,and shed light on promising clinical trials.展开更多
This paper presents a novel approach to improve aliasing rejection in comb-based decimation filters. The method is established on certain palindromic polynomials with all zeros on the unit circle and the sharpening te...This paper presents a novel approach to improve aliasing rejection in comb-based decimation filters. The method is established on certain palindromic polynomials with all zeros on the unit circle and the sharpening technique. As a result, aliasing rejection and the passband characteristic are improved. The method is illustrated with various examples and compared with the methods from the literature. .展开更多
文摘Palindrome number conjecture: Take any non-palindromic natural number with two or more digits, add its inverse ordinal number, continue to use the inverted number of sum plus sum, repeat this process continuously. After a finite number of operations, a palindrome number must be obtained. We firstly give out several definitions: The pure-single-digit-of-sum is the number of single digits that only count the sum of two numbers of the same digit in the vertical operation of addition, which is referred to as pure single digit for short, denoted by g. The pure-carry-digit-of-sum is the carry digit that only counts the sum of two numbers in the same bit in the vertical operation of addition. It is a special number composed of only 1 and 0, which is represented by j'. The complement-0-carry-digit-of-sum is to supplement a 0 on the last side of j' according to the rule of adding bits, which is denoted by j. Therefore, in the addition operation, the sum of any natural number and its inverse ordinal number is divided into two parts: g and j. Then, the characteristics of g and j are characterized by the following two theorems: Theorem 1: As all the numbers in j are 0, j is the palindrome number;As the numbers in j are not all 0, j is not a palindrome number. Theorem 2: The sum of any palindrome number H and any non-palindrome j number must be a non-palindrome number. Then we proved the palindrome number conjecture is not correct by using the above two theorems.
文摘Orphan diseases are rare diseases that affect less than 200000 individuals within the United States.Most orphan diseases are of neurologic and genetic origin.With the current advances in technology,more funding has been devoted to developing therapeutic agents for patients with these conditions.In our review,we highlight emerging options for patients with neurologic orphan diseases,specifically including diseases resulting in muscular deterioration,epilepsy,seizures,neurodegenerative movement disorders,inhibited cognitive development,neuron deterioration,and tumors.After extensive literature review,gene therapy offers a promising route for the treatment of neurologic orphan diseases.The use of clustered regularly interspaced palindromic repeats/Cas9 has demonstrated positive results in experiments investigating its role in several diseases.Additionally,the use of adeno-associated viral vectors has shown improvement in survival,motor function,and developmental milestones,while also demonstrating reversal of sensory ataxia and cardiomyopathy in Friedreich ataxia patients.Antisense oligonucleotides have also been used in some neurologic orphan diseases with positive outcomes.Mammalian target of rapamycin inhibitors are currently being investigated and have reduced abnormal cell growth,proliferation,and angiogenesis.Emerging innovations and the role of genetic treatments open a new window of opportunity for the treatment of neurologic orphan diseases.
文摘Pancreatic cancer(PC)remains one of the most challenging diseases,with a very poor 5-year overall survival of around 11.5%.Kirsten rat sarcoma virus(KRAS)mutation is seen in 90%-95%of PC patients and plays an important role in cancer cell proliferation,differentiation,metabolism,and survival,making it an essential mutation for targeted therapy.Despite extensive efforts in studying this oncogene,there has been little success in finding a drug to target this pathway,labelling it for decades as“undruggable”.In this article we summarize some of the efforts made to target the KRAS pathway in PC,discuss the challenges,and shed light on promising clinical trials.
文摘This paper presents a novel approach to improve aliasing rejection in comb-based decimation filters. The method is established on certain palindromic polynomials with all zeros on the unit circle and the sharpening technique. As a result, aliasing rejection and the passband characteristic are improved. The method is illustrated with various examples and compared with the methods from the literature. .
