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In mathematics , a natural number in a given number base is a p {\displaystyle p} - Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has p {\displaystyle p} digits, that add up to the original number. For example, in base 10 , 45 is a 2-Kaprekar number, because 45² = 2025, and 20 + 25 = 45. The numbers are named after D. R. Kaprekar .
Let n {\displaystyle n} be a natural number. Then the Kaprekar function for base b > 1 {\displaystyle b>1} and power p > 0 {\displaystyle p>0} F p , b : N → N {\displaystyle F_{p,b}:\mathbb {N} \rightarrow \mathbb {N} } is defined to be the following:
where β = n 2 mod b p {\displaystyle \beta =n^{2}{\bmod {b}}^{p}} and
A natural number n {\displaystyle n} is a p {\displaystyle p} - Kaprekar number if it is a fixed point for F p , b {\displaystyle F_{p,b}} , which occurs if F p , b ( n ) = n {\displaystyle F_{p,b}(n)=n} . 0 {\displaystyle 0} and 1 {\displaystyle 1} are trivial Kaprekar numbers for all b {\displaystyle b} and p {\displaystyle p} , all other Kaprekar numbers are nontrivial Kaprekar numbers .
The earlier example of 45 satisfies this definition with b = 10 {\displaystyle b=10} and p = 2 {\displaystyle p=2} , because
A natural number n {\displaystyle n} is a sociable Kaprekar number if it is a periodic point for F p , b {\displaystyle F_{p,b}} , where F p , b k ( n ) = n {\displaystyle F_{p,b}^{k}(n)=n} for a positive integer k {\displaystyle k} (where F p , b k {\displaystyle F_{p,b}^{k}} is the k {\displaystyle k} th iterate of F p , b {\displaystyle F_{p,b}} ), and forms a cycle of period k {\displaystyle k} . A Kaprekar number is a sociable Kaprekar number with k = 1 {\displaystyle k=1} , and a amicable Kaprekar number is a sociable Kaprekar number with k = 2 {\displaystyle k=2} .
The number of iterations i {\displaystyle i} needed for F p , b i ( n ) {\displaystyle F_{p,b}^{i}(n)} to reach a fixed point is the Kaprekar function's persistence of n {\displaystyle n} , and undefined if it never reaches a fixed point.
There are only a finite number of p {\displaystyle p} -Kaprekar numbers and cycles for a given base b {\displaystyle b} , because if n = b p + m {\displaystyle n=b^{p}+m} , where m > 0 {\displaystyle m>0} then
and β = m 2 {\displaystyle \beta =m^{2}} , α = b p + 2 m {\displaystyle \alpha =b^{p}+2m} , and F p , b ( n ) = b p + 2 m + m 2 = n + ( m 2 + m ) > n {\displaystyle F_{p,b}(n)=b^{p}+2m+m^{2}=n+(m^{2}+m)>n} . Only when n ≤ b p {\displaystyle n\leq b^{p}} do Kaprekar numbers and cycles exist.
If d {\displaystyle d} is any divisor of p {\displaystyle p} , then n {\displaystyle n} is also a p {\displaystyle p} -Kaprekar number for base b p {\displaystyle b^{p}} .
In base b = 2 {\displaystyle b=2} , all even perfect numbers are Kaprekar numbers. More generally, any numbers of the form 2 n ( 2 n + 1 − 1 ) {\displaystyle 2^{n}(2^{n+1}-1)} or 2 n ( 2 n + 1 + 1 ) {\displaystyle 2^{n}(2^{n+1}+1)} for natural number n {\displaystyle n} are Kaprekar numbers in base 2 .
The set K ( N ) {\displaystyle K(N)} for a given integer N {\displaystyle N} can be defined as the set of integers X {\displaystyle X} for which there exist natural numbers A {\displaystyle A} and B {\displaystyle B} satisfying the Diophantine equation [ 1 ]
An n {\displaystyle n} -Kaprekar number for base b {\displaystyle b} is then one which lies in the set K ( b n ) {\displaystyle K(b^{n})} .
It was shown in 2000 [ 1 ] that there is a bijection between the unitary divisors of N − 1 {\displaystyle N-1} and the set K ( N ) {\displaystyle K(N)} defined above. Let Inv ( a , c ) {\displaystyle \operatorname {Inv} (a,c)} denote the multiplicative inverse of a {\displaystyle a} modulo c {\displaystyle c} , namely the least positive integer m {\displaystyle m} such that a m = 1 mod c {\displaystyle am=1{\bmod {c}}} , and for each unitary divisor d {\displaystyle d} of N − 1 {\displaystyle N-1} let e = N − 1 d {\displaystyle e={\frac {N-1}{d}}} and ζ ( d ) = d Inv ( d , e ) {\displaystyle \zeta (d)=d\ {\text{Inv}}(d,e)} . Then the function ζ {\displaystyle \zeta } is a bijection from the set of unitary divisors of N − 1 {\displaystyle N-1} onto the set K ( N ) {\displaystyle K(N)} . In particular, a number X {\displaystyle X} is in the set K ( N ) {\displaystyle K(N)} if and only if X = d Inv ( d , e ) {\displaystyle X=d\ {\text{Inv}}(d,e)} for some unitary divisor d {\displaystyle d} of N − 1 {\displaystyle N-1} .
The numbers in K ( N ) {\displaystyle K(N)} occur in complementary pairs, X {\displaystyle X} and N − X {\displaystyle N-X} . If d {\displaystyle d} is a unitary divisor of N − 1 {\displaystyle N-1} then so is e = N − 1 d {\displaystyle e={\frac {N-1}{d}}} , and if X = d Inv ( d , e ) {\displaystyle X=d\operatorname {Inv} (d,e)} then N − X = e Inv ( e , d ) {\displaystyle N-X=e\operatorname {Inv} (e,d)} .
Let k {\displaystyle k} and n {\displaystyle n} be natural numbers, the number base b = 4 k + 3 = 2 ( 2 k + 1 ) + 1 {\displaystyle b=4k+3=2(2k+1)+1} , and p = 2 n + 1 {\displaystyle p=2n+1} . Then:
Let
X 1 = b p − 1 2 = b − 1 2 ∑ i = 0 p − 1 b i = 4 k + 3 − 1 2 ∑ i = 0 2 n + 1 − 1 b i = ( 2 k + 1 ) ∑ i = 0 2 n b i {\displaystyle {\begin{aligned}X_{1}&={\frac {b^{p}-1}{2}}\\&={\frac {b-1}{2}}\sum _{i=0}^{p-1}b^{i}\\&={\frac {4k+3-1}{2}}\sum _{i=0}^{2n+1-1}b^{i}\\&=(2k+1)\sum _{i=0}^{2n}b^{i}\end{aligned}}}
Then,
X 1 2 = ( b p − 1 2 ) 2 = b 2 p − 2 b p + 1 4 = b p ( b p − 2 ) + 1 4 = ( 4 k + 3 ) 2 n + 1 ( b p − 2 ) + 1 4 = ( 4 k + 3 ) 2 n ( b p − 2 ) ( 4 k + 4 ) − ( 4 k + 3 ) 2 n ( b p − 2 ) + 1 4 = − ( 4 k + 3 ) 2 n ( b p − 2 ) + 1 4 + ( k + 1 ) ( 4 k + 3 ) 2 n ( b p − 2 ) = − ( 4 k + 3 ) 2 n − 1 ( b p − 2 ) ( 4 k + 4 ) + ( 4 k + 3 ) 2 n − 1 ( b p − 2 ) + 1 4 + ( k + 1 ) b 2 n ( b 2 n + 1 − 2 ) = ( 4 k + 3 ) 2 n − 1 ( b p − 2 ) + 1 4 + ( k + 1 ) b 2 n ( b p − 2 ) − ( k + 1 ) b 2 n − 1 ( b 2 n + 1 − 2 ) = ( 4 k + 3 ) p − 2 ( b p − 2 ) + 1 4 + ∑ i = p − 2 p − 1 ( − 1 ) i ( k + 1 ) b i ( b p − 2 ) = ( 4 k + 3 ) p − 2 ( b p − 2 ) + 1 4 + ( b p − 2 ) ( k + 1 ) ∑ i = p − 2 p − 1 ( − 1 ) i b i = ( 4 k + 3 ) 1 ( b p − 2 ) + 1 4 + ( b p − 2 ) ( k + 1 ) ∑ i = 1 p − 1 ( − 1 ) i b i = − ( b p − 2 ) + 1 4 + ( b p − 2 ) ( k + 1 ) ∑ i = 0 p − 1 ( − 1 ) i b i = ( b p − 2 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) + − b 2 n + 1 + 3 4 = ( b p − 2 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) + − 4 b 2 n + 1 + 3 b 2 n + 1 + 3 4 = ( b p − 2 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) − b p + 3 b 2 n + 1 + 3 4 = ( b p − 2 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) − b p + 3 ( 4 k + 3 ) p − 2 + 3 4 + 3 ( k + 1 ) ∑ i = p − 2 p − 1 ( − 1 ) i b i = ( b p − 2 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) − b p + 3 ( 4 k + 3 ) 1 + 3 4 + 3 ( k + 1 ) ∑ i = 1 p − 1 ( − 1 ) i b i = ( b p − 2 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) − b p + − 3 + 3 4 + 3 ( k + 1 ) ∑ i = 0 p − 1 ( − 1 ) i b i = ( b p − 2 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) + 3 ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) − b p = ( b p − 2 + 3 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) − b p = ( b p + 1 ) ( k + 1 ) ( ∑ i = 0 2 n ( − 1 ) i b i ) − b p = ( b p + 1 ) ( − 1 + ( k + 1 ) ∑ i = 0 2 n ( − 1 ) i b i ) + 1 = ( b p + 1 ) ( k + ( k + 1 ) ∑ i = 1 2 n ( − 1 ) i b i ) + 1 = ( b p + 1 ) ( k + ( k + 1 ) ∑ i = 1 n b 2 i − b 2 i − 1 ) + 1 = ( b p + 1 ) ( k + ( k + 1 ) ∑ i = 1 n ( b − 1 ) b 2 i − 1 ) + 1 = ( b p + 1 ) ( k + ∑ i = 1 n ( ( k + 1 ) b − k − 1 ) b 2 i − 1 ) + 1 = ( b p + 1 ) ( k + ∑ i = 1 n ( k b + ( 4 k + 3 ) − k − 1 ) b 2 i − 1 ) + 1 = ( b p + 1 ) ( k + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) + 1 = b p ( k + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) + ( k + 1 + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) {\displaystyle {\begin{aligned}X_{1}^{2}&=\left({\frac {b^{p}-1}{2}}\right)^{2}\\&={\frac {b^{2p}-2b^{p}+1}{4}}\\&={\frac {b^{p}(b^{p}-2)+1}{4}}\\&={\frac {(4k+3)^{2n+1}(b^{p}-2)+1}{4}}\\&={\frac {(4k+3)^{2n}(b^{p}-2)(4k+4)-(4k+3)^{2n}(b^{p}-2)+1}{4}}\\&={\frac {-(4k+3)^{2n}(b^{p}-2)+1}{4}}+(k+1)(4k+3)^{2n}(b^{p}-2)\\&={\frac {-(4k+3)^{2n-1}(b^{p}-2)(4k+4)+(4k+3)^{2n-1}(b^{p}-2)+1}{4}}+(k+1)b^{2n}(b^{2n+1}-2)\\&={\frac {(4k+3)^{2n-1}(b^{p}-2)+1}{4}}+(k+1)b^{2n}(b^{p}-2)-(k+1)b^{2n-1}(b^{2n+1}-2)\\&={\frac {(4k+3)^{p-2}(b^{p}-2)+1}{4}}+\sum _{i=p-2}^{p-1}(-1)^{i}(k+1)b^{i}(b^{p}-2)\\&={\frac {(4k+3)^{p-2}(b^{p}-2)+1}{4}}+(b^{p}-2)(k+1)\sum _{i=p-2}^{p-1}(-1)^{i}b^{i}\\&={\frac {(4k+3)^{1}(b^{p}-2)+1}{4}}+(b^{p}-2)(k+1)\sum _{i=1}^{p-1}(-1)^{i}b^{i}\\&={\frac {-(b^{p}-2)+1}{4}}+(b^{p}-2)(k+1)\sum _{i=0}^{p-1}(-1)^{i}b^{i}\\&=(b^{p}-2)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)+{\frac {-b^{2n+1}+3}{4}}\\&=(b^{p}-2)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)+{\frac {-4b^{2n+1}+3b^{2n+1}+3}{4}}\\&=(b^{p}-2)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)-b^{p}+{\frac {3b^{2n+1}+3}{4}}\\&=(b^{p}-2)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)-b^{p}+{\frac {3(4k+3)^{p-2}+3}{4}}+3(k+1)\sum _{i=p-2}^{p-1}(-1)^{i}b^{i}\\&=(b^{p}-2)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)-b^{p}+{\frac {3(4k+3)^{1}+3}{4}}+3(k+1)\sum _{i=1}^{p-1}(-1)^{i}b^{i}\\&=(b^{p}-2)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)-b^{p}+{\frac {-3+3}{4}}+3(k+1)\sum _{i=0}^{p-1}(-1)^{i}b^{i}\\&=(b^{p}-2)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)+3(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)-b^{p}\\&=(b^{p}-2+3)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)-b^{p}\\&=(b^{p}+1)(k+1)\left(\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)-b^{p}\\&=(b^{p}+1)\left(-1+(k+1)\sum _{i=0}^{2n}(-1)^{i}b^{i}\right)+1\\&=(b^{p}+1)\left(k+(k+1)\sum _{i=1}^{2n}(-1)^{i}b^{i}\right)+1\\&=(b^{p}+1)\left(k+(k+1)\sum _{i=1}^{n}b^{2i}-b^{2i-1}\right)+1\\&=(b^{p}+1)\left(k+(k+1)\sum _{i=1}^{n}(b-1)b^{2i-1}\right)+1\\&=(b^{p}+1)\left(k+\sum _{i=1}^{n}((k+1)b-k-1)b^{2i-1}\right)+1\\&=(b^{p}+1)\left(k+\sum _{i=1}^{n}(kb+(4k+3)-k-1)b^{2i-1}\right)+1\\&=(b^{p}+1)\left(k+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)+1\\&=b^{p}\left(k+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)+\left(k+1+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)\end{aligned}}}
The two numbers α {\displaystyle \alpha } and β {\displaystyle \beta } are
and their sum is
α + β = ( k + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) + ( k + 1 + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) = 2 k + 1 + ∑ i = 1 n ( ( 2 k ) b + 2 ( 3 k + 2 ) ) b 2 i − 1 = 2 k + 1 + ∑ i = 1 n ( ( 2 k ) b + ( 6 k + 4 ) ) b 2 i − 1 = 2 k + 1 + ∑ i = 1 n ( ( 2 k ) b + ( 4 k + 3 ) ) b 2 i − 1 + ( 2 k + 1 ) b 2 i − 1 = 2 k + 1 + ∑ i = 1 n ( ( 2 k + 1 ) b ) b 2 i − 1 + ( 2 k + 1 ) b 2 i − 1 = 2 k + 1 + ∑ i = 1 n ( 2 k + 1 ) b 2 i + ( 2 k + 1 ) b 2 i − 1 = 2 k + 1 + ∑ i = 1 2 n ( 2 k + 1 ) b i = ∑ i = 0 2 n ( 2 k + 1 ) b i = ( 2 k + 1 ) ∑ i = 0 2 n b i = X 1 {\displaystyle {\begin{aligned}\alpha +\beta &=\left(k+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)+\left(k+1+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)\\&=2k+1+\sum _{i=1}^{n}((2k)b+2(3k+2))b^{2i-1}\\&=2k+1+\sum _{i=1}^{n}((2k)b+(6k+4))b^{2i-1}\\&=2k+1+\sum _{i=1}^{n}((2k)b+(4k+3))b^{2i-1}+(2k+1)b^{2i-1}\\&=2k+1+\sum _{i=1}^{n}((2k+1)b)b^{2i-1}+(2k+1)b^{2i-1}\\&=2k+1+\sum _{i=1}^{n}(2k+1)b^{2i}+(2k+1)b^{2i-1}\\&=2k+1+\sum _{i=1}^{2n}(2k+1)b^{i}\\&=\sum _{i=0}^{2n}(2k+1)b^{i}\\&=(2k+1)\sum _{i=0}^{2n}b^{i}&=X_{1}\\\end{aligned}}}
Thus, X 1 {\displaystyle X_{1}} is a Kaprekar number.
Let
X 2 = b 2 n + 1 + 1 2 = b 2 n + 1 − 1 2 + 1 = X 1 + 1 {\displaystyle {\begin{aligned}X_{2}&={\frac {b^{2n+1}+1}{2}}\\&={\frac {b^{2n+1}-1}{2}}+1\\&=X_{1}+1\end{aligned}}}
Then,
X 2 2 = ( X 1 + 1 ) 2 = X 1 2 + 2 X 1 + 1 = X 1 2 + 2 X 1 + 1 = b p ( k + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) + ( k + 1 + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) + b p − 1 + 1 = b p ( k + 1 + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) + ( k + 1 + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) {\displaystyle {\begin{aligned}X_{2}^{2}&=(X_{1}+1)^{2}\\&=X_{1}^{2}+2X_{1}+1\\&=X_{1}^{2}+2X_{1}+1\\&=b^{p}\left(k+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)+\left(k+1+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)+b^{p}-1+1\\&=b^{p}\left(k+1+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)+\left(k+1+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)\end{aligned}}}
The two numbers α {\displaystyle \alpha } and β {\displaystyle \beta } are
and their sum is
α + β = ( k + 1 + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) + ( k + 1 + ∑ i = 1 n ( k b + ( 3 k + 2 ) ) b 2 i − 1 ) = 2 k + 2 + ∑ i = 1 n ( ( 2 k ) b + 2 ( 3 k + 2 ) ) b 2 i − 1 = 2 k + 2 + ∑ i = 1 n ( ( 2 k ) b + ( 6 k + 4 ) ) b 2 i − 1 = 2 k + 2 + ∑ i = 1 n ( ( 2 k ) b + ( 4 k + 3 ) ) b 2 i − 1 + ( 2 k + 1 ) b 2 i − 1 = 2 k + 2 + ∑ i = 1 n ( ( 2 k + 1 ) b ) b 2 i − 1 + ( 2 k + 1 ) b 2 i − 1 = 2 k + 2 + ∑ i = 1 n ( 2 k + 1 ) b 2 i + ( 2 k + 1 ) b 2 i − 1 = 2 k + 2 + ∑ i = 1 2 n ( 2 k + 1 ) b i = 1 + ∑ i = 0 2 n ( 2 k + 1 ) b i = 1 + ( 2 k + 1 ) ∑ i = 0 2 n b i = 1 + X 1 = X 2 {\displaystyle {\begin{aligned}\alpha +\beta &=\left(k+1+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)+\left(k+1+\sum _{i=1}^{n}(kb+(3k+2))b^{2i-1}\right)\\&=2k+2+\sum _{i=1}^{n}((2k)b+2(3k+2))b^{2i-1}\\&=2k+2+\sum _{i=1}^{n}((2k)b+(6k+4))b^{2i-1}\\&=2k+2+\sum _{i=1}^{n}((2k)b+(4k+3))b^{2i-1}+(2k+1)b^{2i-1}\\&=2k+2+\sum _{i=1}^{n}((2k+1)b)b^{2i-1}+(2k+1)b^{2i-1}\\&=2k+2+\sum _{i=1}^{n}(2k+1)b^{2i}+(2k+1)b^{2i-1}\\&=2k+2+\sum _{i=1}^{2n}(2k+1)b^{i}\\&=1+\sum _{i=0}^{2n}(2k+1)b^{i}\\&=1+(2k+1)\sum _{i=0}^{2n}b^{i}\\&=1+X_{1}\\&=X_{2}\end{aligned}}}
Thus, X 2 {\displaystyle X_{2}} is a Kaprekar number.
Let m {\displaystyle m} , k {\displaystyle k} , and n {\displaystyle n} be natural numbers, the number base b = m 2 k + m + 1 {\displaystyle b=m^{2}k+m+1} , and the power p = m n + 1 {\displaystyle p=mn+1} . Then:
Let m {\displaystyle m} , k {\displaystyle k} , and n {\displaystyle n} be natural numbers, the number base b = m 2 k + m + 1 {\displaystyle b=m^{2}k+m+1} , and the power p = m n + m − 1 {\displaystyle p=mn+m-1} . Then:
Let m {\displaystyle m} , k {\displaystyle k} , and n {\displaystyle n} be natural numbers, the number base b = m 2 k + m 2 − m + 1 {\displaystyle b=m^{2}k+m^{2}-m+1} , and the power p = m n + m − 1 {\displaystyle p=mn+m-1} . Then:
Let m {\displaystyle m} , k {\displaystyle k} , and n {\displaystyle n} be natural numbers, the number base b = m 2 k + m 2 − m + 1 {\displaystyle b=m^{2}k+m^{2}-m+1} , and the power p = m n + m − 1 {\displaystyle p=mn+m-1} . Then:
All numbers are in base b {\displaystyle b} .
2 → 4 → 2
9 → B → 9
15 → 24 → 15
41 → 50 → 41
4 → 20 → 4
11 → 22 → 11
45 → 56 → 45
10 → 100 → 10000 → 1000 → 10
111 → 10010 → 1110 → 1010 → 111
100 → 10000 → 100
1001 → 10010 → 1001
100101 → 101110 → 100101
100 → 10000 → 100
122012 → 201212 → 122012
10 → 100 → 10000 → 10
1000 → 1000000 → 100000 → 1000
100110 → 101111 → 110010 → 1010111 → 1001100 → 111101 → 100110
10 → 100 → 10000 → 10
1000 → 1000000 → 100000 → 1000
1111121 → 1111211 → 1121111 → 1111121
10 → 100 → 10000 → 100000000 → 10000000 → 100000 → 10
1000 → 1000000 → 1000
10011010 → 11010010 → 10011010
Kaprekar numbers can be extended to the negative integers by use of a signed-digit representation to represent each integer. | https://en.wikipedia.org/wiki/Kaprekar_number |
Kapteyn series is a series expansion of analytic functions on a domain in terms of the Bessel function of the first kind . Kapteyn series are named after Willem Kapteyn , who first studied such series in 1893. [ 1 ] [ 2 ] Let f {\displaystyle f} be a function analytic on the domain
with a < 1 {\displaystyle a<1} . Then f {\displaystyle f} can be expanded in the form
where
The path of the integration is the boundary of D a {\displaystyle D_{a}} . Here Θ 0 ( z ) = 1 / z {\displaystyle \Theta _{0}(z)=1/z} , and for n > 0 {\displaystyle n>0} , Θ n ( z ) {\displaystyle \Theta _{n}(z)} is defined by
Kapteyn's series are important in physical problems. Among other applications, the solution E {\displaystyle E} of Kepler's equation M = E − e sin E {\displaystyle M=E-e\sin E} can be expressed via a Kapteyn series: [ 2 ] [ 3 ]
Let us suppose that the Taylor series of f {\displaystyle f} reads as
Then the α n {\displaystyle \alpha _{n}} coefficients in the Kapteyn expansion of f {\displaystyle f} can be determined as follows. [ 4 ] : 571
The Kapteyn series of the powers of z {\displaystyle z} are found by Kapteyn himself: [ 1 ] : 103, [ 4 ] : 565
For n = 1 {\displaystyle n=1} it follows (see also [ 4 ] : 567 )
and for n = 2 {\displaystyle n=2} [ 4 ] : 566
Furthermore, inside the region D 1 {\displaystyle D_{1}} , [ 4 ] : 559 | https://en.wikipedia.org/wiki/Kapteyn_series |
The Kapustinskii equation calculates the lattice energy U L for an ionic crystal , which is experimentally difficult to determine. It is named after Anatoli Fedorovich Kapustinskii who published the formula in 1956. [ 1 ]
The calculated lattice energy gives a good estimation for the Born–Landé equation; the real value differs in most cases by less than 5%.
Furthermore, one is able to determine the ionic radii (or more properly, the thermochemical radius) using the Kapustinskii equation when the lattice energy is known. This is useful for rather complex ions like sulfate (SO 2− 4 ) or phosphate (PO 3− 4 ).
Kapustinskii originally proposed the following simpler form, which he faulted as "associated with antiquated concepts of the character of repulsion forces". [ 1 ] [ 2 ]
Here, K ' = 1.079 × 10 −4 J·m·mol −1 . This form of the Kapustinskii equation may be derived as an approximation of the Born–Landé equation , below. [ 1 ] [ 2 ]
Kapustinskii replaced r 0 , the measured distance between ions, with the sum of the corresponding ionic radii. In addition, the Born exponent, n , was assumed to have a mean value of 9. Finally, Kapustinskii noted that the Madelung constant , M , was approximately 0.88 times the number of ions in the empirical formula. [ 2 ] The derivation of the later form of the Kapustinskii equation followed similar logic, starting from the quantum chemical treatment in which the final term is 1 − d / r 0 where d is as defined above. Replacing r 0 as before yields the full Kapustinskii equation. [ 1 ] | https://en.wikipedia.org/wiki/Kapustinskii_equation |
KarTrak , sometimes KarTrak ACI ( Automatic Car Identification ) or just ACI was a colored barcode system designed to automatically identify railcars and other rolling stock . KarTrak was made a requirement in North America in 1967, but technical problems led to the abandonment of the system by around 1977.
Railroads have struggled with the tracking of railroad cars across their vast networks, a problem that became worse with the increased growth of systems and movement of rail cars from network to network via interchange . A railroad's car could end up a thousand miles away on another company's tracks. This didn't factor the ever growing fleet of privately owned railroad cars, from companies such as TrailerTrain and Union Tank Car Company , who owned massive fleets of railroad cars, but were not actually railroads. A missing car took time to track down, often requiring workers to walk rail yards looking at cars until it was located.
In 1959 David Jarrett Collins approached his employer GTE Sylvania to use a newly developed computer system in conjunction with scanners to track railroad cars. [ 1 ] The idea was inspired by Collins summers in college where he worked for the Pennsylvania Railroad . [ 1 ] During the early portion of the 1960s, Sylvania's Applied Research Lab team met with representatives of various railroads to gain insight into their needs and wants for a car tracking system.
Features and design aspects desired by the railroads included: [ 1 ]
KarTrak's development testing occurred in 1961 on the Boston & Maine Railroad, using passenger trains and a gravel train that did not leave the Boston & Maine railroad network. [ 1 ] Using trains that were always confined to Boston & Maine enabled easy testing, refinement and demonstration the KarTrak system, as cars fitted with the system were always around and their movements known. [ 1 ]
Sylvania early on moved to sell KarTrak to smaller, 'captive' railroad systems. [ 1 ] Captive railroads [ a ] , such as those used to supply coal to a power station on an isolated system were a prime environment, as issues caused by cars not equipped by KarTrak wouldn't occur due to the lack of cars entering or leaving the railroad, and all cars being owned by the railroad in question and thus able to be equipped with labels. In three years, 50,000 railroad cars were equipped KarTrak labels. [ 1 ] This served a dual purpose, allowing Sylvania to generate money to invest in further development of the system, while also denying a foothold to competing car tracking systems.
KarTrak was also be advertised to railroads in publications such as Fortune , and The Wall Street Journal in large, full page ads pushing the monetary and efficiency benefits. [ 2 ] [ 3 ]
By the mid to late 1960s, railroads in North America began searching for a system that would allow them to automatically identify railcars and other rolling stock. Through the efforts of the Association of American Railroads (AAR), a number of companies developed automatic equipment identification (AEI) systems. The AAR selected four systems for extensive field tests:
All those systems, except the RFID system, had labels that were mounted on each side of the railcar, and a trackside scanner. [ 1 ]
Following disagreements with Sylvania regarding the future potential of KarTrak, Collins departed in 1968 to form his own company to continue research and development into scanners and barcodes. [ 1 ] [ 5 ]
After the initial field tests, the ABEX, Wabco, and GTE KarTrak ACI systems were selected for a head-to-head accuracy test on the Pennsylvania Railroad , at Spruce Creek, Pennsylvania . The KarTrak system was declared the winner and selected by the AAR as the standard. [ 1 ]
Starting in 1967, all railcar owners were required by the AAR to install ACI labels on their cars. By 1970, roughly 86% of the 2 million railroad freight cars were carrying an ACI plate, with some railroads having completed labeling of their freight cars. Twelve railroads had completed installation of approximately 50 ACI trackside scanners. [ 6 ]
In 1972, GTE Sylvania decided to exit the railcar tracking field, and sold KarTrak to Servo Corporation of America. [ 7 ]
By 1975, 90% of all railcars were labeled. The read rate was about 80%, which means that after seven years of service, 10% of the labels had failed for reasons such as physical damage and dirt accumulation. The dirt accumulation was most evident on flatcars that had low-mounted labels.
The AAR had recognized from their field tests that periodic inspection and label maintenance would be requirements to maintain a high level of label readability. Regulations were instituted for label inspection and repair whenever a railcar was in the repair shop, which on average happened every two years. The maintenance program never gained sufficient compliance. Without maintenance, the read rate failed to improve, and the KarTrak system was abandoned by 1977.
Even towards the end of and after the demise of KarTrak, development of improvements based on the system did continue, with three patents being issued in 1976, 1977 and 1982 that were based on the KarTrak technology, one for a variable label that could signal an issue with car, like a refrigerator car that was too warm, a self cleaning ACI label, and a three-dimensional 'optical target' as another attempt to eliminate the known issue with dirty labels. [ 8 ] [ 9 ] [ 10 ]
In November 1977, the Association of American Railroads released a short white paper that flagged several problems with KarTrak: Frequent inaccuracies in data, ACI labels reaching the end of their life span and requiring replacement, and lack of universal adoption within the railroad industry. A weighted ballot would be conducted of all interchange railroads, weighted based on ownership of railcars, to if the ACI requirements would be eliminated. [ 11 ] The result of this ballot was to eliminate the requirement to install ACI labels. The decision was overwhelming, with a 5 to 1 margin. [ 12 ] Despite claiming in their white paper that the dissatisfaction with ACI "would not mean the railroad industry was taking a step backward in car utilization, or operating efficiency or in the adoption of modern technology." of this failure, the railroad industry did not seriously search for another system to identify railcars until the mid-1980s. [ 12 ] [ 3 ]
KarTrak ACI tags consisted of a plate with 13 horizontal labels put in a vertical arrangement that are also understood as data lines, which could have 13 different forms. These labels, or symbols, stand for the single digits 0-9, the number 10 as an extra feature for the checksum line, and the "START" and "STOP" labels that gave reference to the vertical line position of the tag. [ 13 ] Present day available depictions of the labels do often name the upper color first and then the lower color.
In practice people found that there was a significant number of cases where the label set was not done correctly or the label application had errors such as a 180° rotation of it - whilst as a rule of thumbs the blue stripes of START and STOP would have been needed to point to the left with a to-the-middle-of-the-tag orientation. Especially the color selection and sequence ordering of STOP seems to be the subject of such errors leading to decoding errors and needs for decoder workarounds for the field that effectively weakened the system. Even some early times advertisement materials exposed such flaws. Also its said that checksum labels had been wrong sometimes, and even the label set itself had some variations in respect to the imprinted number.
- = not used / reserved white = white/black checker pattern aka checkered
The labels, also understood as data lines, each had two horizontal stripes that together represented a single symbol of information. The used colors for the stripes were blue, white, red and black. This does make up a total of 16 combinations where only 12 were used in the center area by just excluding black to be the lower color. For sensor reasons the white color was dimmed down by a black checkerboard so that they roughly met with the intensity of red and blue that were light sensed via a color filters.
The labels each are 5 + 3 ⁄ 4 inches (15 cm) wide and 1 inch (2.5 cm) high. With a 3 ⁄ 8 inch (0.95 cm) vertical gap between the labels realized a total height of 17.5 inches (44 cm). Labels could be affixed directly to the car side, but usually were applied to dark plates, which were then riveted to each side of the car. [ 14 ]
The labels were made from retroreflective plastic sheet that was coated with red or blue dye to provide distinguishable color filters. The retroreflective material gave a clear optical signal that could be read from a 9-to-12-foot (2.7 to 3.7 m) distance and easily distinguished from the other markings on the railcar. The white areas provided both a red and blue optical response to the reader, and were patterned with dots so that their brightness would be about the same as a red or blue stripe.
The start and stop labels were partially filled, so that the reader scanning beam would be centered on them before they were recognized. This ensured that the entire label was centered and had the best chance of being read accurately.
The labels are to be read from bottom to top:
The first digit of the equipment owner (line 2) marks the type of equipment: 0 for railroad-owned, 1 for privately-owned, or 6 for non-revenue equipment.
The car number is left-padded with zeroes if necessary. For locomotives, line 6 is the type of unit and line 7 the suffix number.
The check digit is calculated as follows: Each number digit is multiplied by two to the power of the labels's position minus two . Thus, the first digit (line 2) is multiplied by 1, the second by 2, the third by 4, the fourth by 8 and so on, until the 10th, which is multiplied by 512. The sum of all these numbers modulo 11 is the check digit. [ 13 ]
The code on the caboose in the picture at top can be decoded as Start 8350199918 Stop 5 . This means a car with equipment code number 8, ownership code 350, which lists this as a car of the Illinois Central Railroad , [ 15 ] car number 199918, with a check digit of 5.
Labels were placed on both sides of all railroad equipment, including locomotives, passenger cars, and cabooses . Labels were required to be unobstructed, and couldn't have anything such as ladders, railings, grab iron between them and the scanner. When placed on rail cars with external [ 16 ] For curved surfaces of tank cars, an oversized ACI label was available, known as a 'extended-range panel' The retroreflective stripes on these panels were 3.5 inches (89 mm) taller than standard stripes. [ 16 ]
The readers were optical scanners, somewhat like the barcode scanners used for retail store barcode items today. The scanning distances and speeds meant that the processing electronics needed to be state-of-the-art for its day. They were placed along the rail lines, often at the entrance and exit of a switchyard and at major junctions, spaced back from the tracks so that the labels would pass in the reading zone, 9 to 12 feet (2.7 to 3.7 m) from the scanner and with the scanner aperture at 9 feet 6 inches (2.90 m) above the railhead. [ 17 ]
The scanners were housed in metal boxes typically about the size of a mini-refrigerator, 24 by 24 by 12 inches (610 by 610 by 300 mm). [ 17 ] They consisted of a collimated 100-200 watt xenon arc light source arranged co-axially with red and blue sensing photo tubes. The coaxial optical arrangement provided optimum sensing of the retroreflective labels. This optical source and sensing beam was directed to a large (8–14 in or 20–36 cm) mirrored rotating wheel that provided the vertical scanning of the railcar. The movement of the train provided the horizontal scanning. Although the system could capture labels at 60 miles per hour (97 km/h), often the speeds were much lower. [ 18 ]
The scanner's analog video signals were passed to a nearby rail equipment hut where the processing and computing electronics were located. [ 19 ] [ 20 ] The first systems were discrete circuits and logic and only provided an ASCII -coded list of the labels that passed the scanner. These were forwarded to the rail operators for manual tracking or integration with their computer systems. Later reading systems were coupled with era minicomputers ( Digital Equipment Corporation PDP-8s ), and more elaborate tracking and weighing systems were integrated. Sometimes these included many railyard input sensors, for rail switch position, car passage, and hot wheel bearing sensors. Some of the more productive and thus longer-lived systems were installed in captive rail applications that carried bulk goods from mines to smelter, where the weight of individual cars loaded and unloaded tracked the bulk inventory.
The KarTrak system proved to need too much maintenance to be practical. Up to 20% of the cars were not read correctly. Further, ACI did not have any centralized system or network, even within railroad companies. The information collected from wayside scanners was printed out with little means of searching for information beyond going through piles of paperwork. Clerical personnel became frustrated by the increasing error rate. These issues would lead to the abandonment by the ARR who discontinued the requirement for rail cars to have KarTrak labels. Between 1967 and 1977, the railroad industry spent $150 million on KarTrak, and up to 95% of cars were barcoded. [ 3 ]
Railroad cars that were in service prior to 1977 would go on to carry KarTrak labels, with labels being still observed on freight cars into the 2000s. [ 21 ] These labels have vanished in time due to a combination of repainting, major overhaul, and the retirement of cars, particularly due to the AAR Rule 88 and 90, which restrict use of rail cars built prior to July 1, 1974 to a 40-year life, which ran out for most cars in the mid-2010s. Cars built on and after 1 July 1974 are subject to a 50-year life, with mandatory retirements to start in 2024. [ 22 ] [ 23 ]
Versions of KarTrak technology were trialed in other fields. In the late 1960s, the New Jersey Turnpike explored the system as a way of billing vehicles using the toll road , as well as identifying the vehicle. A computer would calculate the toll due and a bill would be sent to the driver. [ 24 ] Like the original version of KarTrak, vehicles would be fitted with a label approximately 3 by 7 inches (76 by 178 mm) that would be scanned by a camera at toll booths .
In 1984, Computer Identics Corporation, Collins' company following his departure from GTE Sylvania, would sue Southern Pacific Transportation, along with three other companies, alleging they'd acted in a conspiracy to intentionally undermine KarTrak, in favor of a system Southern Pacific had been working on called TOPS . The lawsuit was ultimately unsuccessful, with the jury having found there was no evidence of a conspiracy, which was then upheld on appeal. [ 25 ] | https://en.wikipedia.org/wiki/KarTrak |
The Karachi Institute of Power Engineering , commonly known as KINPOE , [ 1 ] is a post-graduate applied science school of the Institute of Engineering and Applied Sciences . [ 2 ] Established by the Pakistan Atomic Energy Commission (PAEC) in 1993 with cooperation with the NED University of Engineering and Technology in Karachi , the school grants the post-graduate degrees and training certifications in power engineering related disciplines. [ 3 ] The school is located near the vicinity of the Karachi Nuclear Power Complex (KANUPP-II) near at Paradise Point in Karachi , Pakistan . [ 4 ]
This Pakistan university, college or other higher education institution article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karachi_Institute_of_Power_Engineering |
In mathematics , Karamata's inequality , [ 1 ] named after Jovan Karamata , [ 2 ] also known as the majorization inequality , is a theorem in elementary algebra for convex and concave real-valued functions, defined on an interval of the real line. It generalizes the discrete form of Jensen's inequality , and generalizes in turn to the concept of Schur-convex functions .
Let I be an interval of the real line and let f denote a real-valued, convex function defined on I . If x 1 , …, x n and y 1 , …, y n are numbers in I such that ( x 1 , …, x n ) majorizes ( y 1 , …, y n ) , then
Here majorization means that x 1 , …, x n and y 1 , …, y n satisfies
and we have the inequalities
and the equality
If f is a strictly convex function , then the inequality ( 1 ) holds with equality if and only if we have x i = y i for all i ∈ {1, …, n } .
x ⪯ w y {\displaystyle x\preceq _{w}y} if and only if ∑ g ( x i ) ≤ ∑ g ( y i ) {\displaystyle \sum g\left(x_{i}\right)\leq \sum g\left(y_{i}\right)} for any continuous increasing convex function g : R → R {\displaystyle g:\mathbb {R} \to \mathbb {R} } . [ 3 ]
The finite form of Jensen's inequality is a special case of this result. Consider the real numbers x 1 , …, x n ∈ I and let
denote their arithmetic mean . Then ( x 1 , …, x n ) majorizes the n -tuple ( a , a , …, a ) , since the arithmetic mean of the i largest numbers of ( x 1 , …, x n ) is at least as large as the arithmetic mean a of all the n numbers, for every i ∈ {1, …, n − 1} . By Karamata's inequality ( 1 ) for the convex function f ,
Dividing by n gives Jensen's inequality. The sign is reversed if f is concave.
We may assume that the numbers are in decreasing order as specified in ( 2 ).
If x i = y i for all i ∈ {1, …, n } , then the inequality ( 1 ) holds with equality, hence we may assume in the following that x i ≠ y i for at least one i .
If x i = y i for an i ∈ {1, …, n } , then the inequality ( 1 ) and the majorization properties ( 3 ) and ( 4 ) are not affected if we remove x i and y i . Hence we may assume that x i ≠ y i for all i ∈ {1, …, n } .
It is a property of convex functions that for two numbers x ≠ y in the interval I the slope
of the secant line through the points ( x , f ( x )) and ( y , f ( y )) of the graph of f is a monotonically non-decreasing function in x for y fixed (and vice versa ). This implies that
for all i ∈ {1, …, n − 1} . Define A 0 = B 0 = 0 and
for all i ∈ {1, …, n } . By the majorization property ( 3 ), A i ≥ B i for all i ∈ {1, …, n − 1} and by ( 4 ), A n = B n . Hence,
which proves Karamata's inequality ( 1 ).
To discuss the case of equality in ( 1 ), note that x 1 > y 1 by ( 3 ) and our assumption x i ≠ y i for all i ∈ {1, …, n − 1} . Let i be the smallest index such that ( x i , y i ) ≠ ( x i +1 , y i +1 ) , which exists due to ( 4 ). Then A i > B i . If f is strictly convex, then there is strict inequality in ( 6 ), meaning that c i +1 < c i . Hence there is a strictly positive term in the sum on the right hand side of ( 7 ) and equality in ( 1 ) cannot hold.
If the convex function f is non-decreasing, then c n ≥ 0 . The relaxed condition ( 5 ) means that A n ≥ B n , which is enough to conclude that c n ( A n − B n ) ≥ 0 in the last step of ( 7 ).
If the function f is strictly convex and non-decreasing, then c n > 0 . It only remains to discuss the case A n > B n . However, then there is a strictly positive term on the right hand side of ( 7 ) and equality in ( 1 ) cannot hold.
An explanation of Karamata's inequality and majorization theory can be found here . | https://en.wikipedia.org/wiki/Karamata's_inequality |
The Karatmeter is a scientific instrument which uses X-rays to give an exact reading of the purity of gold . The Karatmeter is also referred to as a X-Ray fluorescence (XRF) spectrometer. Due to its very high precision and fast result, X-ray analysis has been adopted by international agencies in India as part of the certification process used to hallmark gold. [ 1 ] It is an accurate, non-destructive means of testing the purity of gold and other related elements. Analyzing gold using XRF spectrometers gives the purity of gold, up to 10-12 microns and hence it gives the analysis of coating only.
Using this technique, the precise percentage or karat (of karat ) in a solid piece of jewelry can be determined in 30 seconds. It also accurately (up to 10-12 microns) determines the element composition of all types of gold, white gold , platinum , silver , palladium , rhodium and related alloys .
Energy dispersive X-Ray fluorescence (ED-XRF) is a simple, accurate and economic analytical methods for the determination of the chemical composition of many types of materials. It is non-destructive and reliable, requires very little sample preparation and is suitable for solid, liquid and powdered samples. It can be used for a wide range of elements, from Chlorine (17) to Uranium (92), and provides detection limits at the sub-ppm level.
There are many models of Gold Purity Testing machines available - from portable (light weight) to industrial grade machines.
Apart from X-ray spectrometer technique, other older traditional methods are using the TouchStone and Acid to test the gold purity. But TouchStone and Acid are destructive testing - a tiny sample of gold is cut and then tested. The sample is rubbed on TouchStone and a drop of acid is put on it and the goldsmith observes the residue using a magnifying lens. Based on experience, gold smith can determine purity of sample.
This physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karatmeter |
In Indian astronomy, a karaṇa is a half of a tithi . It is the duration of time in which the difference of the longitudes of the Sun and the Moon is increased by 6 degrees. [ 1 ] [ 2 ] A lunar month has 30 tithi -s and so the number of karaṇa -s in a lunar month is 60. These sixty karaṇa -s are not individually named. Instead, the originators of the concept have chosen 11 names to be associated with the karaṇa -s which means several karaṇa -s will be associated with the same name. Of these 11 names, four are fixed or immovables (or sthira -s) in the sense that they are associated with four unique karaṇa -s in a lunar month. These constant names are Śakuni , Catuṣpāda , Nāga and Kimstughna . The remaining seven names are variable or movable (or, cara -s) in the sense that there are several karaṇa -s associated with each of them. These names are Bava , Bālava , Kaulava , Taitila , Gara , Vaṇij and Vṛṣṭi .
The four fixed names are assigned as follows:
The fifty-six half tithi -s starting from Śukla pakṣa pratipad second half to Kṛṣṇa pakṣa caturdasi first half are given the variable names Bava , Bālava , Kaulava , Taitila , Gara , Vaṇij and Vṛṣṭi in a cyclical order. These names are repeated in the same order eight times so that the same name is assigned to eight different half tithi -s.
The fixed and variable names are assigned as in the following table.
The name of the karaṇa at a particular moment on any given day can be determined by the following algorithm. [ 2 ]
In the Malayalam astronomical literature, the eleven karaṇas are assigned names which are words for various animals. The English equivalents of the animal words representing the various karaṇas are given below. [ 3 ]
Most probably the concept of karaṇa arose almost simultaneously with the concept of tithi . Tithi -s are related to lunar-days and lunar-days are similar in concept to solar days or sāvana days. A sāvana day is the duration of time from one sunrise to the next sunrise. Roughly one half of a sāvana day is the duration of time from sunrise to the next sunset and the other half is the duration of time from sunset to the next sunrise. Before the introduction of the modern concept of tithi , the concept of a lunar day was in vogue. It was the duration of time from one moon-rise to the next moon-rise. Similar to the division of a sāvana day, the lunar-day can also be divided into two halves: One half being the duration of time from moon-rise to the next moon-set (the lunar day time) and the other half being the duration of time from moon-set to the next moon-rise (lunar night time). The concept of karaṇa has originated in this division of the lunar day. Later, when the concept of tithi got established, the concepts of the lunar day time and lunar night time got replaced by the modern artificial concept of half- tithi -s. The works of the Vedāṅga period - Atharva Jyotiṣa and Ṛk-pariśiṣṭa mention the karaṇa -s. So the origination of the oncept of karaṇa -s can be traced to as early as the period of Vedāṅga Jyotiṣa , that is, around 500 BCE. [ 4 ] [ 5 ] | https://en.wikipedia.org/wiki/Karaṇa_(pañcāṅga) |
In mathematics , the Kardar–Parisi–Zhang (KPZ) equation is a non-linear stochastic partial differential equation , introduced by Mehran Kardar , Giorgio Parisi , and Yi-Cheng Zhang in 1986. [ 1 ] [ 2 ] It describes the temporal change of a height field h ( x → , t ) {\displaystyle h({\vec {x}},t)} with spatial coordinate x → {\displaystyle {\vec {x}}} and time coordinate t {\displaystyle t} :
Here, η ( x → , t ) {\displaystyle \eta ({\vec {x}},t)} is white Gaussian noise with average
⟨ η ( x → , t ) ⟩ = 0 {\displaystyle \langle \eta ({\vec {x}},t)\rangle =0}
and second moment
⟨ η ( x → , t ) η ( x → ′ , t ′ ) ⟩ = 2 D δ d ( x → − x → ′ ) δ ( t − t ′ ) , {\displaystyle \langle \eta ({\vec {x}},t)\eta ({\vec {x}}',t')\rangle =2D\delta ^{d}({\vec {x}}-{\vec {x}}')\delta (t-t'),}
ν {\displaystyle \nu } , λ {\displaystyle \lambda } , and D {\displaystyle D} are parameters of the model, and d {\displaystyle d} is the dimension.
In one spatial dimension, the KPZ equation corresponds to a stochastic version of Burgers' equation with field u ( x , t ) {\displaystyle u(x,t)} via the substitution u = − λ ∂ h / ∂ x {\displaystyle u=-\lambda \,\partial h/\partial x} .
Via the renormalization group , the KPZ equation is conjectured to be the field theory of many surface growth models, such as the Eden model , ballistic deposition, and the weakly asymmetric single step solid on solid process (SOS) model. A rigorous proof has been given by Bertini and Giacomin in the case of the SOS model. [ 3 ]
Many interacting particle systems , such as the totally asymmetric simple exclusion process , lie in the KPZ universality class . This class is characterized by the following critical exponents in one spatial dimension (1 + 1 dimension): the roughness exponent α = 1 2 {\displaystyle \alpha ={\tfrac {1}{2}}} , growth exponent β = 1 3 {\displaystyle \beta ={\tfrac {1}{3}}} , and dynamic exponent z = 3 2 {\displaystyle z={\tfrac {3}{2}}} . In order to check if a growth model is within the KPZ class, one can calculate the width of the surface:
where h ¯ ( t ) {\displaystyle {\bar {h}}(t)} is the mean surface height at time t {\displaystyle t} and L {\displaystyle L} is the size of the system. For models within the KPZ class, the main properties of the surface h ( x , t ) {\displaystyle h(x,t)} can be characterized by the Family – Vicsek scaling relation of the roughness [ 4 ]
with a scaling function f ( u ) {\displaystyle f(u)} satisfying
In 2014, Hairer and Quastel showed that more generally, the following KPZ-like equations lie within the KPZ universality class: [ 2 ]
where P {\displaystyle P} is any even-degree polynomial .
A family of processes that are conjectured to be universal limits in the (1+1) KPZ universality class and govern the long time fluctuations are the Airy processes and the KPZ fixed point .
Due to the nonlinearity in the equation and the presence of space-time white noise , solutions to the KPZ equation are known to not be smooth or regular, but rather ' fractal ' or ' rough .' Even without the nonlinear term, the equation reduces to the stochastic heat equation , whose solution is not differentiable in the space variable but satisfies a Hölder condition with exponent less than 1/2. Thus, the nonlinear term ( ∇ h ) 2 {\displaystyle \left(\nabla h\right)^{2}} is ill-defined in a classical sense.
In 2013, Martin Hairer made a breakthrough in solving the KPZ equation by an extension of the Cole–Hopf transformation and constructing approximations using Feynman diagrams . [ 5 ] In 2014, he was awarded the Fields Medal for this work on the KPZ equation, along with rough paths theory and regularity structures . There were 6 different analytic self-similar solutions found for the (1+1) KPZ equation with different analytic noise terms. [ 6 ]
This derivation is from [ 7 ] and. [ 8 ] Suppose we want to describe a surface growth by some partial differential equation . Let h ( x , t ) {\displaystyle h(x,t)} represent the height of the surface at position x {\displaystyle x} and time t {\displaystyle t} . Their values are continuous. We expect that there would be a sort of smoothening mechanism. Then the simplest equation for the surface growth may be taken to be the diffusion equation ,
But this is a deterministic equation, implying the surface has no random fluctuations. The simplest way to include fluctuations is to add a noise term. Then we may employ the equation
with η {\displaystyle \eta } taken to be the Gaussian white noise with mean zero and covariance E [ η ( x , t ) η ( x ′ , t ′ ) ] = δ ( x − x ′ ) δ ( t − t ′ ) {\displaystyle E[\eta (x,t)\eta (x',t')]=\delta (x-x')\delta (t-t')} . This is known as the Edwards–Wilkinson (EW) equation or stochastic heat equation with additive noise (SHE). Since this is a linear equation , it can be solved exactly by using Fourier analysis . But since the noise is Gaussian and the equation is linear, the fluctuations seen for this equation are still Gaussian. This means the EW equation is not enough to describe the surface growth of interest, so we need to add a nonlinear function for the growth. Therefore, surface growth change in time has three contributions. The first models lateral growth as a nonlinear function of the form F ( ∂ h ( x , t ) ∂ x ) {\displaystyle F\left({\frac {\partial h(x,t)}{\partial x}}\right)} . The second is a relaxation , or regularization , through the diffusion term ∂ 2 h ( x , t ) ∂ 2 x {\displaystyle {\frac {\partial ^{2}h(x,t)}{\partial ^{2}x}}} , and the third is the white noise forcing η ( x , t ) {\displaystyle \eta (x,t)} . Therefore,
The key term F ( ∂ h ( x , t ) ∂ x ) {\displaystyle F\left({\frac {\partial h(x,t)}{\partial x}}\right)} , the deterministic part of the growth, is assumed to be a function only of the slope, and to be a symmetric function . A great observation of Kardar, Parisi, and Zhang (KPZ) [ 1 ] was that while a surface grows in a normal direction (to the surface), we are measuring the height on the height axis, which is perpendicular to the space axis, and hence there should appear a nonlinearity coming from this simple geometric effect. When the surface slope ∂ x h = ∂ h ∂ x {\displaystyle \partial _{x}h={\tfrac {\partial h}{\partial x}}} is small, the effect takes the form F ( ∂ x h ) = ( 1 + | ∂ x h | 2 ) − 1 2 {\displaystyle F(\partial _{x}h)=(1+|\partial _{x}h|^{2})^{-{\frac {1}{2}}}} , but this leads to a seemingly intractable equation. To circumvent this difficulty, one can take a general F {\displaystyle F} and expand it as a Taylor series ,
The first term can be removed from the equation by a time shift, since if h ( x , t ) {\displaystyle h(x,t)} solves the KPZ equation, then h ~ ( x , t ) := h ( x , t ) − λ F ( 0 ) t {\displaystyle {\tilde {h}}(x,t):=h(x,t)-\lambda F(0)t} solves
The second should vanish because of the symmetry of F {\displaystyle F} , but could anyway have been removed from the equation by a constant velocity shift of coordinates, since if h ( x , t ) {\displaystyle h(x,t)} solves the KPZ equation, then h ~ ( x , t ) := h ( x − λ F ′ ( 0 ) t , t − λ F ′ ( 0 ) x ) {\displaystyle {\tilde {h}}(x,t):=h(x-\lambda F'(0)t,t-\lambda F'(0)x)} solves
Thus the quadratic term is the first nontrivial contribution, and it is the only one kept. We arrive at the KPZ equation | https://en.wikipedia.org/wiki/Kardar–Parisi–Zhang_equation |
Karen K. Hsiao Ashe is a professor at the Department of Neurology and Neuroscience at the University of Minnesota (UMN) Medical School , where she holds the Edmund Wallace and Anne Marie Tulloch Chairs in Neurology and Neuroscience. [ 2 ] She is the founding director of the N. Bud Grossman Center for Memory Research and Care, [ 2 ] [ 3 ] and her specific research interest is memory loss resulting from Alzheimer's disease and related dementias . [ 2 ] [ 1 ] Her research has included the development of an animal model of Alzheimer's. [ 1 ] [ 4 ]
In July 2022, concerns were raised that certain images in a 2006 Nature paper [ 5 ] co-authored by Ashe and her postdoctoral student Sylvain Lesné were manipulated. [ 6 ] In May 2023, the Star Tribune reported that Ashe was using new techniques to re-do the work reported in the 2006 Nature study, this time without Lesné, and that she stated "it's my responsibility to establish the truth of what we've published". [ 7 ] The new article was published in March 2024. [ 8 ] The 2006 article was retracted in June 2024; all of the original authors except Lesné agreed with the retraction. [ 9 ] [ 10 ]
Ashe's parents came to the United States from China in 1943 to pursue PhDs, before settling in the Minneapolis–Saint Paul area. Her father, C.C. Hsiao , taught aerospace engineering at the University of Minnesota, and her mother, Joyce, was a biochemist. [ 1 ] [ 11 ] She has three younger siblings. [ 1 ]
Attending the St. Paul Academy and Summit School in the 1970s, Ashe's interest in the brain began in primary school, where she excelled in math, along with music. [ 1 ] She obtained her undergraduate degree at Harvard University [ 2 ] in 1975 in chemistry and physics, [ 12 ] starting as a sophomore at the age of 17. [ 1 ] She went on to earn her PhD in brain and cognitive sciences at MIT in 1981 and her MD from Harvard in 1982. [ 12 ] [ 1 ]
Ashe's husband, James, is a neurologist; she has three children (two sons and a daughter). [ 1 ]
Between 1986 and 1989, she was a post-doctoral fellow at the University of California, San Francisco where she researched prion diseases and published with Stanley Prusiner . [ 2 ] [ 1 ] [ 12 ] In 1989, she was the first author on a paper published in Nature , entitled "Linkage of a prion protein missense variant to Gerstmann‑Sträussler syndrome ", describing the discovery of a mutation linked to a neurodegenerative disease . [ 13 ] She was the first author on a paper published in 1990 in Science , entitled "Spontaneous neurodegeneration in transgenic mice with mutant prion protein", describing the creation of a transgenic mouse modeling a neurodegenerative disease. [ 14 ] According to the Minneapolis Star Tribune , she helped prove Prusiner's theory that prions cause neurodegenerative diseases . [ 1 ] Prusiner recognized her contribution towards the Nobel Prize he won for that work, [ 1 ] saying that Karen Hsiao "discovered a mutation in the PrP gene that caused familial disease and reproduced the disease in transgenic mice". [ 15 ]
Ashe joined the University of Minnesota Medical School in 1992 as an assistant professor of neurology. [ 1 ] She has also worked with the Minneapolis Veterans Affairs Health Care System . [ 1 ] She was the founding director of the N. Bud Grossman Center for Memory Research and Care. [ 2 ] [ 3 ] [ 16 ] As of 2022, she has received over $28 million in grants from the U.S. National Institutes of Health . [ 17 ]
The Minneapolis Star Tribune described Ashe as a "distinguished professor considered by many to be on the short list for a Nobel Prize for her work". [ 18 ]
In 1996—early in her career at UMN—Ashe was the first author on a paper published in Science , entitled "Correlative memory deficits, Aβ elevation, and amyloid plaques in transgenic mice", [ 19 ] describing a mouse model of Alzheimer's disease , which furthered her rising star as a scientist; the mice are used in research around the world, and students and scientists "come from all over the world to work with her", according to the Star Tribune . [ 1 ] In 2006, three of her research papers made a list of the eighteen papers that had contributed the most to Alzheimer's research. [ 20 ]
Ashe is a co-author on a 2006 paper published in Nature (retracted in 2024 [ 10 ] ), entitled "A specific amyloid-β protein assembly in the brain impairs memory". [ 6 ] [ 5 ] The paper describes the Aβ*56 oligomer (known as amyloid beta star 56 and Aβ*56 ) correlating with memory loss in mice prior to the appearance of amyloid plaques . According to a Science article, in 2022 the paper was the fifth-highest cited paper in Alzheimer's research, with approximately 2,300 other articles citing it. [ 6 ] The Guardian says the paper was "highly influential" and calls it "one of the most cited pieces of Alzheimer's disease research in the last two decades", writing that it has "dominated the field" of research. [ 21 ] The Daily Telegraph states that the "seminal research paper" led to increased drug research funding worldwide. [ 22 ] The paper was discussed at the Alzheimer Research Forum as a "star is born". [ 6 ] [ 23 ]
In 2015, Ashe was a co-author on a paper entitled "Quaternary structure defines a large class of amyloid-beta oligomers neutralized by sequestration", which defines two forms of Aβ based on quaternary structure, type 1 and type 2, that have different effects on memory function in mice. [ 24 ] Type 1 is dispersed in the brain and associated with impaired memory. Type 2 is entrapped in amyloid plaques and does not impair memory. [ 24 ] [ 25 ] In 2020, she published a review summarizing this work, entitled "The biogenesis and biology of amyloid β oligomers in the brain". [ 25 ]
In July 2022, concerns were raised by Matthew Schrag , a Vanderbilt University neuroscientist, [ 18 ] that certain images in the 2006 Nature paper were manipulated [ 6 ] in the paper co-authored by Ashe's postdoctoral Sylvain Lesné , whom she hired in 2002. [ 6 ] [ 26 ] These concerns were published in an article in Science authored by Charles Piller which questioned the association between the Aβ*56 protein and dementia symptoms. [ 6 ] Ashe stated in July 2022 via email that "it is devastating to discover that a colleague may have misled me and the scientific community [... it is also] distressing that a major scientific journal has blatantly misrepresented the implications of my work." [ 17 ] [ Note 1 ] Ashe has stated that the edited images, which she agrees "should not have occurred", [ 27 ] do not change the conclusions of the paper. [ 28 ] No image inconsistencies have been found in other work published by Ashe without Lesné as a co-author. [ 6 ]
UMN is investigating the reports [ 21 ] as of May 2023. [ 29 ] The editors of Nature responded with a July 14, 2022 note stating they were aware of and investigating the concerns raised, that a "further editorial response [would] follow as soon as possible", and that "readers are advised to use caution when using results reported therein". [ 5 ] [ 17 ] The NIH, where Schrag lodged the whistleblower report, is also investigating the matter. [ 22 ] Retraction Watch states that Ashe co-authored with Lesné other disputed papers, and that the authors in the disputed work do not overlap except for two from UMN Department of Neuroscience. [ 30 ]
In May 2023, the Star Tribune reported that Ashe was using new techniques to re-do the work reported in the 2006 Nature study, this time without Lesné, and that she stated "it's my responsibility to establish the truth of what we've published". [ 29 ] Ashe's new article was published in March 2024 in the journal iScience . [ 8 ]
In May 2024, Ashe announced that the 2006 publication would be retracted because Nature would not print a correction . [ 10 ] According to Retraction Watch , this makes it the most highly cited paper ever retracted. [ 10 ] Piller reported in Science that Ashe "and colleagues claim to confirm the findings of the 2006 paper", and Ashe states that "the manipulated images did not affect the study conclusions". [ 10 ] All of the original authors except Lesné agreed to the June 2024 retraction; [ 9 ] other researchers dispute the strength of conclusions in the new, re-worked study. [ 10 ]
Ashe was awarded the Metlife Foundation Award for Medical Research in Alzheimer's Disease in 2005. [ 31 ] Ashe also earned the Potamkin Prize in 2006 for her Alzheimer's research, [ 32 ] [ 33 ] shortly after the publication of the 2006 Nature paper. [ 6 ]
In 2009, Ashe was elected to the National Academy of Medicine for her achievements in medicine. [ 34 ] | https://en.wikipedia.org/wiki/Karen_Ashe |
Karen Chan is an associate professor at the Technical University of Denmark . [ 2 ] She is a Canadian and French physicist most notable for her work on catalysis , electrocatalysis, and electrochemical reduction of carbon dioxide .
Chan earned her B.Sc. in Chemical Physics in 2007 and her PhD in Chemistry in 2013 from Simon Fraser University under Michael Eikerling. [ citation needed ]
Chan is known for her theoretical and computational work on the description of solid-liquid interfaces, electrocatalysis, batteries, and heterogeneous catalysis. Her work on computer simulations of the electrical double-layer and electrocatalysis has led to new ideas and understanding of, for instance, electrochemical carbon dioxide reduction , [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] and water electrolysis . [ 8 ] [ 9 ]
Following the completion of her PhD, she served as a postdoctoral researcher at Stanford University and in 2016 was promoted to staff scientist at SLAC National Accelerator Laboratory . In October 2018, she began serving as an associate professor at the Technical University of Denmark . [ 10 ] | https://en.wikipedia.org/wiki/Karen_Chan |
Joseph Black Award (2013)
Top 50 Women in Analytical Science (2016)
Coblentz Society Craver Award (2016)
The Analytical Scientist Top 10 Spectroscopists (2017)
Karen Jane Faulds FRSE is a Scottish academic and Professor of Analytical Chemistry at the University of Strathclyde . [ 1 ] [ 2 ] [ 3 ] She develops surface-enhanced Raman spectroscopy (SERS) for bioanalysis, and has won several awards for her research, including the Coblentz Society Craver Award.
Faulds studied forensic and analytical science at the University of Strathclyde , graduating with a BSc in 1998. [ 4 ] She remained at Strathclyde for her doctoral studies and in 2003 received her PhD for research on the detection of drugs of substance abuse using surface-enhanced Raman spectroscopy (SERS). [ 5 ]
Faulds worked as a postdoctoral researcher for Duncan Graham [ Wikidata ] on the detection of DNA using surface-enhanced resonant Raman spectroscopy (SERRS). [ 6 ] She became increasingly interested in the use of analytical chemistry to improve people's lives. Faulds was appointed as a lecturer in 2006. [ 7 ] [ 8 ]
Faulds was promoted to Reader in 2012 and Professor in 2015. [ 7 ] Faulds works on the development of surface-enhanced Raman spectroscopy (SERS) for analytical detection. [ 9 ] SERSs permits multiplexed and sensitive biological analysis. [ 10 ] Her work uses signal amplification methods for the quantitative analysis of biomolecules, as the sensitivity allows her to detect target DNA and proteins . [ 11 ] [ 12 ] SERS also allows Faulds to make multiple measurements of different analytes in one sample. [ 13 ] [ 14 ] In 2015 she was the first woman and youngest person to ever be elected chair of the Infrared and Raman Discussion Group (IRDG). [ 15 ] She has described C. V. Raman as her "hero of spectroscopy". [ 6 ]
Her recent work has looked at the optical detection of Listeria using bionanosensors . [ 16 ] The bionanosensors permit the multiplexed detection of pathogens , which can remove the risk of infectious diseases without the need for antimicrobial drugs. [ 17 ] She covers SERS active magnetic nanoparticles with lectins, which can recognise and bind to carbohydrates in bacteria . [ 17 ] These nanoparticles can collect and concentrate bacteria from production lines. [ 17 ] Silver nanoparticles are functionalised with a biorecognition molecule, such as an aptamer , and Raman reporter, resulting in a SERS signal when a nanoparticle binds to the bacterial target. [ 17 ] The magnetic component can then be studied further using portable Raman spectrometers . [ 17 ]
Faulds is a founding member of Renishaw plc diagnostics, a University of Strathclyde spin-off company, and serves as its Director of Research. [ 18 ] Faulds joined the editorial board of RSC Advances in November 2016 [ 19 ] and as Associate Editor of Analyst in August 2020. [ 20 ] She co-directs the Engineering and Physical Sciences Research Council (EPSRC) and Medical Research Council (MRC) Centre for Doctoral Training (CDT) in Optical Medical Imaging , shared between the University of Edinburgh and the University of Strathclyde . [ 21 ]
Faulds is a Fellow of the Society for Applied Spectroscopy (SAS) and a member of the Young Academy of Scotland (YAS). [ 28 ] [ 7 ]
In 2019 Faulds was included in the 2019 Power List of The Analytical Scientist. [ 29 ] | https://en.wikipedia.org/wiki/Karen_Faulds |
Karen Hao is an American journalist. Currently a freelancer for publications like The Atlantic and previously a foreign correspondent based in Hong Kong for The Wall Street Journal and senior artificial intelligence editor at the MIT Technology Review , she is best known for her coverage on AI research, technology ethics and the social impact of AI. [ 2 ] [ 3 ] Hao also co-produced the podcast In Machines We Trust and wrote the newsletter The Algorithm. [ 4 ]
Previously, she worked at Quartz as a tech reporter and data scientist and was an application engineer at the first startup to spin out of X Development . Hao's writing has also appeared in Mother Jones , Sierra Magazine , The New Republic , and other publications.
Hao graduated from The Lawrenceville School in 2011. [ 5 ] She studied at the Massachusetts Institute of Technology , graduating with a B.S. in mechanical engineering and a minor in energy studies in 2015. [ 6 ] She is a native speaker in both English and Mandarin Chinese. [ 2 ]
Hao is known in the technology world for her coverage of new AI research findings and their societal and ethical impacts. Her writing has spanned research and issues regarding big tech data privacy , misinformation , deepfakes , facial recognition , and AI healthcare tools.
In March 2021, Hao published a piece that uncovered previously unknown information about how attempts to combat misinformation by different teams at Facebook's using machine learning were impeded and constantly at odds by Facebook's drive to grow user engagement. [ 7 ] [ 8 ] [ 9 ] Upon its release, leaders at Facebook including Mike Schroepfer and Yann LeCun immediately criticized the piece through Twitter responses. [ 10 ] AI researchers and AI ethics experts Timnit Gebru and Margaret Mitchell responded in support of Hao's writing and advocated for more change and improvement for all. [ 11 ]
Hao also co-produced the podcast In Machines We Trust , which discusses the rise of AI with people developing, researching, and using AI technologies. [ 12 ] The podcast won the 2020 Front Page Award in investigative reporting. [ 13 ]
Hao has occasionally created data visualizations that have been featured in her work at the MIT Technology Review and elsewhere. In 2018, her "What is AI?" flowchart visualization was exhibited as an installation at the Museum of Applied Arts in Vienna . [ 14 ]
She has been an invited speaker at TEDxGateway , the United Nations Foundation , EmTech , WNPR , and many other conferences and podcasts. [ 15 ] [ 16 ] Her TEDx talk discussed the importance of democratizing how AI is built. [ 17 ]
In March 2022, she was hired by The Wall Street Journal to cover China technology and society, while being based in Hong Kong . [ 18 ] | https://en.wikipedia.org/wiki/Karen_Hao |
The Karen Harvey Prize is awarded by the American Astronomical Society 's Solar Physics Division in recognition for a significant contribution to the study of the Sun early in a person's professional career.
Past winners are: [ 1 ]
This science awards article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karen_Harvey_Prize |
Karen Helen Wiltshire (born 1962) is an Irish environmental scientist . She is professor for shelf-ecosystems and was one of the vice directors of Alfred Wegener Institute for Polar and Marine Research (AWI). [ 1 ]
Born in Dublin , Wiltshire studied at Trinity College Dublin and graduated with a master's degree in environmental science. She received her Ph.D. and habilitation (2001) in hydrobiology at the University of Hamburg . She worked as a postdoctoral fellow at the GKSS Geesthacht [ de ] , the University of St. Andrews, Scotland and was appointed Professor of Geosciences at Jacobs University in 2006. [ 2 ]
Wiltshire supports Scientists for Future in Germany and took part in a statement at the Bundespressekonferenz in March 2019. [ 3 ]
In 2024, Wiltshire was appointed CRH Chair of Climate Science in Trinity College Dublin. In 2025, she was made a fellow of Trinity College Dublin. [ 4 ] | https://en.wikipedia.org/wiki/Karen_Helen_Wiltshire |
Karen Dale Williams Morse is a inorganic chemist. She was president of Western Washington University from 1993 until 2008, and was named the Bowman Distinguished Professor in 2014. She is an elected fellow of the American Association for the Advancement of Science .
Morse has a B.A. from Denison University (1962), and an M.S. and Ph.D. from the University of Michigan . [ 1 ] During her Ph.D. she worked on Lewis acids . [ 2 ] Morse joined the faculty of Utah State University in 1968 in the department of chemistry and biochemistry, [ 3 ] and subsequently became the department head, the dean, [ 4 ] and was named provost in 1989. [ 5 ] [ 3 ] In 1993 she moved to Western Washington University where she was president until 2008. [ 3 ] In 2014, Morse was named the Bowman Distinguished Professor at Western Washington University. [ 6 ]
Morse's early research centered on the production [ 7 ] and properties [ 8 ] of phosphines . She also worked on borohydrides , [ 9 ] [ 10 ] phosphite, [ 11 ] metal-phosphorus compounds, [ 12 ] [ 13 ] aryl phosphines [ 14 ] Morse also led the professional training committee at the American Chemical Society where she expanded on options for recognizing educators who teach chemistry at the undergraduate and high school level. [ 15 ] [ 16 ]
Morse was elected a fellow of the American Association for the Advancement of Science in 1986. [ 17 ] In 1997 she received the Garvan–Olin Medal for scientific accomplishments by a woman chemist from the American Chemical Society . [ 18 ] In 2012 Western Washington University named the chemistry building the Karen W. Morse Hall in recognition of her. [ 19 ] In 2021, Utah State University awarded her with an honorary doctorate. [ 4 ] | https://en.wikipedia.org/wiki/Karen_Morse_(chemist) |
Karin Erdmann (born 1948) is a German mathematician specializing in the areas of algebra known as representation theory (especially modular representation theory ) and homological algebra (especially Hochschild cohomology ). She is notable for her work in modular representation theory which has been cited over 1500 times according to the Mathematical Reviews . Her nephew Martin Erdmann is professor for experimental particle physics at the RWTH Aachen University .
She attended the Justus-Liebig-Universität Gießen and wrote her Ph.D. thesis on " 2-Hauptblöcke von Gruppen mit Dieder-Gruppen als 2-Sylow-Gruppen " (Principal 2-blocks of groups with dihedral Sylow 2-subgroups ) in 1976 under the direction of Gerhard O. Michler . [ 1 ]
Erdmann was a Fellow of Somerville College, Oxford . Erdmann is a university lecturer emeritus at the Mathematical Institute at the University of Oxford where she has had 25 doctoral students and 45 descendants. [ 1 ] She has published over 115 papers and her work has been cited over 2000 times. [ 2 ] She has contributed to the understanding of the representation theory of the symmetric group .
Erdmann was the inaugural Emmy Noether Lecturer of the German Mathematical Society in 2008. [ 3 ]
This article about a German mathematician is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karin_Erdmann |
Karin Lochte (born 20 September 1952) is a German oceanographer , researcher, and climate change specialist. [ 1 ] [ 2 ] She was director of German Polar Research Alfred Wegener Institute from 2007 to 2017 as well as chairman of the management committee of Jacobs University Bremen . [ 2 ]
Lochte was born in Hanover . She received her PhD in marine biology at the University College of North Wales in 1984.
After her PhD, she worked on deep sea microbiology at the Institut für Meereskunde, University of Kiel . Earlier in her career, Lochte was a professor of Biological Oceanography at the Leibniz Institute for Marine Sciences at the Christian-Albrechts University in Kiel where she led a research unit that focused on chemical cycles in the sea. She lectured biological oceanography at the University of Rostock and Kiel from 1995 to 2000 and subsequently at the Leibniz Institute for Baltic Sea Research in Warnemünde until 2007. She was also the project coordinator for the Atlantic Data Base for Exchange Processes at the Deep Sea Floor (ADEPD), a European Union funded marine research project from 1998 to 2000. Her involvement in polar research began in 2007, when she started work at the Alfred Wegener Institute in Bremerhaven . [ 2 ] [ 3 ]
Lochte was appointed as the Director of the Alfred Wegener Institute in 2007 and hold that position to 2017. [ 2 ] [ 4 ] Her research focussed on the interactions between ocean nutrient cycles and climate. [ 1 ] She has been the vice-president of Earth and Environment field research for the Helmholtz Association . [ 5 ]
Lochte is a member of several national and international boards, scientific committees and research funding organizations. She was a member of the German Scientific Council, which advises the German Federal and state Governments and the on development of universities, science and research and is chair of the Scientific Commission of Lower Saxony . She is also a delegate of the Scientific Committee on Antarctic Research and chairperson of the Board of Governors of Jacobs University . [ 6 ] She is on the advisory board of the Arctic Circle . [ 7 ] [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/Karin_Lochte |
Karin Ingegerd Öberg (born August 27, 1982) is a Swedish astrochemist . [ 1 ] She is a Professor of Astronomy at Harvard University and leader of the Öberg Astrochemistry Group at the Center for Astrophysics | Harvard & Smithsonian . [ 2 ] Her research concerns star formation , planet formation , and stellar evolution in relation to organic molecules , which are necessary to determine the origins of life on Earth and elsewhere. [ 3 ] [ 4 ] In April 2015, her group discovered the first complex organic molecule in a protoplanetary disk. [ 2 ] [ 5 ] [ 6 ]
Karin Öberg was born in Nyköping, Sweden . [ 1 ] At age 6, her family relocated to Karlskrona , where she spent the rest of her childhood. [ 1 ] She was raised alongside two brothers, and attended public primary, secondary, and high schools. [ 1 ] In 2001, Öberg's high school chemistry teacher signed her up for the local Chemistry Olympiad . She qualified for the international competition, being one of four students to represent Sweden. [ 7 ] Also during her senior year at the Chapmanskolan gymnasium , she conducted a project under the supervision of her father, which resulted in her first publication . [ 1 ]
Öberg was educated at the California Institute of Technology and graduated cum laude in 2005 with a Bachelor of Science degree in Chemistry . [ 8 ] She has said that "Caltech was a birth through fire experience into science, which taught [her] to think, to ask questions, and to solve problems as [she] scarce had thought [her] mind capable of." [ 1 ] During her time as an undergraduate, she was a member of physical chemistry and astrochemistry research, [ 1 ] and published two scientific papers based on her work in the groups. [ 1 ]
Following her undergraduate studies, Öberg took up a Ph.D. position at Leiden University in the Netherlands under the supervision of Ewine van Dishoeck and Harold Linnartz. [ 1 ] She spent four years combining laboratory simulation and astronomical observation to study the chemistry and dynamics of interstellar ice . [ 4 ] This research led to a thesis , titled "Complex processes in simple ices: Laboratory and observational studies of gas-grain interactions during star formation." [ 1 ] Öberg presented the different chapters at conferences worldwide and several institutions in the United States. [ 1 ] The doctoral thesis was defended on September 16, 2009. [ 1 ] Besides conducting this research, Öberg supervised two M.Sc. projects and served as a teaching assistant for courses on Pulsars and research for undergraduate students. [ 1 ] She graduated cum laude with a Ph.D. in Astronomy from Leiden University in 2009. [ 8 ]
After Öberg received her Ph.D. in 2009, NASA awarded her a Hubble Postdoctoral Fellowship . [ 9 ] She used this funding to research at the Center for Astrophysics | Harvard & Smithsonian until August 2012. [ 8 ] During this time, she studied the radioastronomical observations of organic molecules in young stars, such as protoplanetary disks and protostars . [ 4 ]
Next, Öberg worked at the University of Virginia as a visiting scholar and Assistant Professor of Chemistry and Astronomy until June 2013. [ 8 ] She conducted laboratory ice experiments and studied spatially- and spectrally-determined astronomical observations, both of which focused on the processes that take place during the chemical evolution of a planet or star. [ 4 ]
Öberg returned to Harvard in July 2013 as an Assistant Professor of Astronomy. [ 8 ] Here, she formed the Öberg Astrochemistry Group. [ 8 ] This group conducts research at the Center for Astrophysics | Harvard & Smithsonian . [ 8 ]
Öberg serves on the board of the Society of Catholic Scientists, [ 10 ] and is an advisor of the Purposeful Universe Project. [ 11 ]
As of 2021, Öberg has published over 130 refereed articles, at least 36 of those as the first author, and has been cited over 11,000 times. [ 12 ] [ 13 ] Her main domain of work currently pertains to astrochemistry and its effect on planet formation . [ 14 ] The Öberg Astrochemistry Group, her current research group, states that their main research addresses the following: [ 3 ]
1. the chemical evolution present during star and planet formation and its effects on planet compositions,
2. the fundamental physical chemical processes that underpin this evolution,
3. and the development of new molecular probes of different aspects of star and planet formation.
The group's research is composed of laboratory ice simulations and radio and infrared observations of astronomical behaviors and information. [ 3 ]
On April 9, 2015, the Öberg Astrochemistry Group published a paper stating they detected the first complex carbon molecule in a protoplanetary disk , this molecule being methyl cyanide . [ 2 ] [ 5 ] Methyl cyanide (CH 3 CN) is thought to be important for the origins of life because it contains carbon-nitrogen bonds , which make up amino acids , the building blocks of proteins . [ 15 ] Up until this discovery, it was unclear if these molecules could exist in abundance in young disks because of their turbulent and chaotic nature. [ 15 ] Using the Atacama Large Millimeter/submillimeter Array (ALMA) , Öberg's group was able to survey the orbital debris of the newly formed star MWC 480, to discover enough methyl cyanide to fill all of Earth's oceans and the presence of other simpler molecules such as hydrogen cyanide . [ 5 ] [ 15 ] [ 16 ] This discovery is significant because it shows that the backbone of life, complex carbon bonds, are not exclusive to our Solar System. [ 5 ] In an interview, Öberg stated that comet records suggest the presence of complex organic molecules in other protoplanetary disks as well. [ 16 ]
The finding was published in the scientific journal Nature (volume 520), titled "The comet-like composition of a protoplanetary disk as revealed by complex cyanides." [ 5 ] It also had media coverage in The Washington Post and LA Times , along with a press release from the National Radio Astronomy Observatory (NRAO) . [ 6 ] [ 17 ] [ 18 ]
As a child, Öberg was confirmed in the Church of Sweden , but soon after became agnostic. [ 19 ] Her later conversion to Catholicism was partly inspired by G. K. Chesterton 's Orthodoxy , [ 19 ] having remained a devout Catholic ever since. [ 20 ] | https://en.wikipedia.org/wiki/Karin_Öberg |
Karl A. Smith is a metallurgical engineer, academic and author. He is an emeritus Cooperative Learning Professor of Engineering Education at Purdue University 's School of Engineering Education, [ 1 ] as well as an emeritus Professor of Civil, Environmental, and Geo-Engineering , Morse-Alumni Distinguished University Teaching Professor, [ 2 ] and Faculty Member at the Technological Leadership Institute at the University of Minnesota . [ 3 ]
Smith's work has focused on developing research and innovation capabilities in engineering education, exploring cooperation in learning and design, and managing projects and knowledge. [ 4 ] His publications comprise research articles and eight books including Teamwork and Project Management , How to Model it: Problem Solving for the Computer Age and New Paradigms for College Teaching . He is the recipient of the University of Minnesota Distinguished Alumni Award (2006), an Honorary Doctorate from the Universiti Teknologi Malaysia (2014) [ 5 ] along with the Chester F. Carlson Award (2001), [ 6 ] the Distinguished Service Award (2006), [ 7 ] and the Lifetime Achievement Award (2015), all from the American Society for Engineering Education . [ 8 ]
Smith is a Fellow of the American Association for the Advancement of Science [ 9 ] and the American Society for Engineering Education, [ 10 ] where he was inducted into the Hall of Fame in 2023. [ 11 ] He served as the Guest Editor of a Special Issue of the Journal of Engineering Education , and as the Editor-in-Chief of Annals of Research on Engineering Education (AREE) . [ 12 ]
Smith earned a BS in Metallurgical Engineering from Michigan Technological University in 1969, subsequently working at an engineering firm in Moab, Utah . He returned to Michigan Tech to complete an M.S. degree in 1972 and then moved to Minneapolis for a research position at the University of Minnesota. [ 13 ]
Smith continued his academic career as an assistant professor at the University of Minnesota in 1980, later becoming associate professor in 1986 and Professor in 2004. In 2011 he served as Distinguished Engineering Education Innovation (E 2 I) Fellow at the Hong Kong University of Science and Technology . He retired from the University of Minnesota in 2011 and between 2006 and 2022 he served as Cooperative Learning Professor of Engineering Education at Purdue University's School of Engineering Education. [ 1 ] Also since 2011, he has held positions as an emeritus Professor of Civil, Environmental, and Geo-Engineering, Morse-Alumni Distinguished University Teaching Professor, [ 2 ] and Faculty Member at the Technological Leadership Institute at the University of Minnesota. [ 3 ] Additionally, in collaboration with Tony Starfield, Alan Wassyng, Sam Sharp, and others, he developed the civil engineering systems and "How to model it" courses for upper division and first-year students, respectively, which, alongside his work in cooperative learning and teamwork with David W. and Roger T. Johnson, led to the creation of the Civil Engineering Project Management course and the Management of Technology Project and Knowledge Management course. [ 14 ] [ 15 ]
Between 1999 and 2004, he had a split appointment with Michigan State University where he served as a Senior Consultant to the Provost for Faculty Development. At the University of Minnesota, he was the Co-coordinator of the Bush Faculty Development Program for Excellence and Diversity in Teaching from 1996 to 1997, Director of undergraduate studies in the Department of Civil Engineering from 1999 to 2004, and executive co-director and researcher in the STEM Education Research Center from 2012 to 2018. [ 16 ] He was inducted into the Michigan Technological University Academy for Engineering Education Leadership in 2018. [ 17 ]
Smith has focused his research on mineral processing technology along with engineering education by facilitating faculty and graduate student professional growth, exploring the role of cooperation in learning and design, addressing problem formulation, modeling, and knowledge engineering, and managing projects and knowledge. [ 4 ]
Smith's contributions to engineering education encompass work in cooperative learning and knowledge engineering applications. He published a paper in the Journal of Engineering Education , in 1981, introducing cooperative learning in engineering literature. [ 18 ] During the early 1980s, he conducted some of the first randomized design empirical studies on cooperative learning in engineering classes. Subsequently, in the late 1980s, he transitioned from engineering research to education research, particularly focusing on cooperative learning and structured controversy, as his emphasis shifted towards teaching and research on project and knowledge management. [ 19 ] This research addressed the critical needs of enhancing student learning, deepening understanding, and fostering collaborative skills. [ 20 ] Beyond cooperative learning, his work included structured academic controversy, aimed at facilitating comprehensive understanding of complex issues through argument development and cooperative learning strategies. [ 21 ] [ 22 ]
Smith published books on this topic, including Active Learning: Cooperation in the College Classroom with David W. Johnson and Roger T. Johnson, providing strategies for college faculty to implement cooperative learning. They also co-authored Cooperative learning: Increasing College Faculty Instructional Productivity , in which they delved into the basics of cooperative learning, and he discussed how cooperative learning changed college teaching in New Paradigms for College Teaching that he co-edited with William E. Campbell. Later, in 2000, he wrote Teamwork and Project Management , where he emphasized key skills for engineering success, including teamwork, problem-solving, and project management. [ 23 ]
Smith worked on the development of technically and environmentally sound mineral and waste processing technologies. He laid the groundwork for various technical innovations, including a carbochlorination technique proposed for use in the processing of lunar anorthite . [ 24 ] Alongside colleagues, he confirmed graphite's ability, with or without catalysts, to selectively reduce iron oxide in synthetic ilmenite, observed through isothermal weight loss over time from 850 °C to 1200 °C under argon atmosphere. [ 25 ] Additionally, he explored reduction roasting processes using various reductants and desulfurizers to convert sulfide minerals to metallic form without sulfur dioxide emissions, capturing sulfur as either calcium sulfide or sodium sulfide . [ 26 ] | https://en.wikipedia.org/wiki/Karl_A._Smith |
Karl Andreas Hofmann (2 April 1870 – 15 October 1940) was a German inorganic chemist. [ 1 ] He is best known for his discovery of a family of clathrates which consist of a 2-D metal cyanide sheet, with every second metal also bound axially to two other ligands. These materials have been named ' Hofmann clathrates ' in his honour.
This article about a German chemist is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karl_Andreas_Hofmann |
Karl Barry Sharpless (born April 28, 1941) is an American stereochemist . He is a two-time Nobel laureate in chemistry , known for his work on stereoselective reactions and click chemistry .
Sharpless was awarded half of the 2001 Nobel Prize in Chemistry "for his work on chirally catalysed oxidation reactions ", and one third of the 2022 prize, jointly with Carolyn R. Bertozzi and Morten P. Meldal , "for the development of click chemistry and bioorthogonal chemistry ". [ 1 ] [ 2 ] Sharpless is the fifth person (in addition to two organizations) to have twice been awarded a Nobel prize, along with Marie Curie , John Bardeen , Linus Pauling and Frederick Sanger , and the third to have been awarded two prizes in the same discipline (after Bardeen and Sanger).
Sharpless was born April 28, 1941, in Philadelphia , Pennsylvania. [ 3 ] His childhood was filled with summers at his family cottage on the Manasquan River in New Jersey . This is where Sharpless developed a love for fishing that he would continue throughout his life, spending summers in college working on fishing boats. [ 4 ] He graduated from Friends' Central School in 1959, [ 5 ] and continued his studies at Dartmouth College , earning an A.B. degree in 1963. Sharpless originally planned to attend medical school after his undergraduate degree, but his research professor convinced him to continue his education in chemistry. [ 6 ] He earned his Ph.D. in organic chemistry from Stanford University in 1968 under Eugene van Tamelen . [ 7 ] He continued post-doctoral work at Stanford University (1968–1969) with James P. Collman , working on organometallic chemistry. Sharpless then moved to Harvard University (1969–1970), studying enzymology in Konrad E. Bloch 's lab. [ 6 ]
Sharpless was a professor at the Massachusetts Institute of Technology (1970–1977, 1980–1990) and Stanford University (1977–1980). [ 8 ] While at Stanford, Sharpless discovered Sharpless asymmetric epoxidation , which was used to make (+)-disparlure. As of 2023 [update] , Sharpless led a laboratory at Scripps Research . [ 9 ]
Sharpless developed stereoselective oxidation reactions, and showed that the formation of an inhibitor with femtomolar potency can be catalyzed by the enzyme acetylcholinesterase , beginning with an azide and an alkyne. He discovered several chemical reactions which have transformed asymmetric synthesis from science fiction to the relatively routine, including aminohydroxylation, dihydroxylation, and the Sharpless asymmetric epoxidation. [ 10 ]
In 2001 he was awarded a half-share of the Nobel Prize in Chemistry for his work on chirally catalyzed oxidation reactions ( Sharpless epoxidation , Sharpless asymmetric dihydroxylation , Sharpless oxyamination ). The other half of the year's Prize was shared between William S. Knowles and Ryōji Noyori (for their work on stereoselective hydrogenation ). [ 1 ]
The term " click chemistry " was coined by Sharpless around the year 2000, and was first fully described by Sharpless, Hartmuth Kolb , and M.G. Finn at The Scripps Research Institute in 2001. [ 11 ] [ 2 ] This involves a set of highly selective, exothermic reactions which occur under mild conditions; the most successful example is the azide alkyne Huisgen cycloaddition to form 1,2,3-triazoles . [ 12 ]
As of 2024 [update] , Sharpless has an h-index of 130 according to Scopus . [ 13 ]
Sharpless is a two-time Nobel laureate. He is a recipient of the 2001 and 2022 Nobel Prize in Chemistry for his work on "chirally catalysed oxidation reactions", and " click chemistry ", respectively. [ 1 ] [ 2 ]
He was awarded the 2001 Wolf Prize in Chemistry together with Henri B. Kagan and Ryoji Noyori “for their pioneering, creative and crucial work in developing asymmetric catalysis for the synthesis of chiral molecules, greatly increasing humankind´s ability to create new products of fundamental and practical importance”.
In 2019, Sharpless was awarded the Priestley medal , the American Chemical Society's highest honor, for "the invention of catalytic, asymmetric oxidation methods, the concept of click chemistry and development of the copper-catalyzed version of the azide-acetylene cycloaddition reaction.". [ 5 ] [ 6 ] He received the Gold Medal of the American Institute of Chemists in 2023. [ 14 ]
He is Distinguished University Professor at Kyushu University . He holds honorary degrees from the KTH Royal Institute of Technology (1995), Technical University of Munich (1995), Catholic University of Louvain (1996) and Wesleyan University (1999). [ 8 ]
Sharpless married Jan Dueser in 1965 and they have three children. [ 10 ] He was blinded in one eye during a lab accident in 1970 where an NMR tube exploded, shortly after he arrived at MIT as an assistant professor. After this accident, Sharpless stresses "there's simply never an adequate excuse for not wearing safety glasses in the laboratory at all times ." [ 15 ] | https://en.wikipedia.org/wiki/Karl_Barry_Sharpless |
In analytical chemistry , Karl Fischer titration is a classic titration method that uses coulometric or volumetric titration to determine trace amounts of water in a sample. It was invented in 1935 by the German chemist Karl Fischer . [ 1 ] [ 2 ] Today, the titration is done with an automated Karl Fischer titrator.
The elementary reaction responsible for water quantification in the Karl Fischer titration is oxidation of sulfur dioxide ( SO 2 ) with iodine :
This elementary reaction consumes exactly one molar equivalent of water vs. iodine. Iodine is added to the solution until it is present in excess, marking the end point of the titration, which can be detected by potentiometry. The reaction is run in an alcohol solution containing a base, which consumes the sulfur trioxide and hydroiodic acid produced.
The main compartment of the titration cell contains the anode solution plus the analyte. The anode solution consists of an alcohol (ROH), a base (B), sulfur dioxide ( SO 2 ) and KI. Typical alcohols that may be used include ethanol , diethylene glycol monoethyl ether , or methanol , sometimes referred to as Karl Fischer grade . A common base is imidazole .
The titration cell also consists of a smaller compartment with a cathode immersed in the anode solution of the main compartment. The two compartments are separated by an ion-permeable membrane.
The Pt anode generates I 2 from the KI when current is provided through the electric circuit. The net reaction as shown below is oxidation of SO 2 by I 2 . One mole of I 2 is consumed for each mole of H 2 O . In other words, 2 moles of electrons are consumed per mole of water.
The end point is detected most commonly by a bipotentiometric titration method. A second pair of Pt electrodes is immersed in the anode solution. The detector circuit maintains a constant current between the two detector electrodes during titration. Prior to the equivalence point, the solution contains I − but little I 2 . At the equivalence point, excess I 2 appears and an abrupt voltage drop marks the end point. The amount of charge needed to generate I 2 and reach the end point can then be used to calculate the amount of water in the original sample.
The volumetric titration is based on the same principles as the coulometric titration, except that the anode solution above now is used as the titrant solution. The titrant consists of an alcohol (ROH), base (B), SO 2 and a known concentration of I 2 . Pyridine has been used as the base in this case.
One mole of I 2 is consumed for each mole of H 2 O . The titration reaction proceeds as above, and the end point may be detected by a bipotentiometric method as described above.
The popularity of the Karl Fischer titration (henceforth referred to as KF) is due in large part to several practical advantages that it holds over other methods of moisture determination, such as accuracy, speed and selectivity.
KF is selective for water, because the titration reaction itself consumes water. In contrast, measurement of mass loss on drying will detect the loss of any volatile substance. However, the strong redox chemistry ( SO 2 /I 2 ) means that redox-active sample constituents may react with the reagents. For this reason, KF is unsuitable for solutions containing e.g. dimethyl sulfoxide .
KF has a high accuracy and precision, typically within 1% of available water, e.g. 3.00% appears as 2.97–3.03%. Although KF is a destructive analysis, the sample quantity is small and is typically limited by the accuracy of weighing. For example, in order to obtain an accuracy of 1% using a scale with the typical accuracy of 0.2 mg, the sample must contain 20 mg water, which is e.g. 200 mg for a sample with 10% water. For coulometers , the measuring range is from 1–5 ppm to about 5%. Volumetric KF readily measures samples up to 100%, but requires impractically large amounts of sample for analytes with less than 0.05% water. [ 3 ] The KF response is linear. Therefore, single-point calibration using a calibrated 1% water standard is sufficient and no calibration curves are necessary.
Little sample preparation is needed: a liquid sample can usually be directly injected using a syringe. The analysis is typically complete within a minute. However, KF suffers from an error called drift , which is an apparent water input that can confuse the measurement. The glass walls of the vessel adsorb water, and if any water leaks into the cell, the slow release of water into the titration solution can continue for a long time. Therefore, before measurement, it is necessary to carefully dry the vessel and run a 10–30-minute "dry run" in order to calculate the rate of drift. The drift is then subtracted from the result.
KF is suitable for measuring liquids and, with special equipment, gases. The major disadvantage with solids is that the water has to be accessible and easily brought into methanol solution. Many common substances, especially foods such as chocolate, release water slowly and with difficulty, requiring additional efforts to reliably bring the total water content into contact with the Karl Fischer reagents. For example, a high-shear mixer may be installed to the cell in order to break the sample. KF has problems with compounds with strong binding to water, as in water of hydration, for example with lithium chloride , so KF is unsuitable for the special solvent LiCl/ DMAc .
KF is suitable for automation. Generally, KF is conducted using a separate KF titrator, or for volumetric titration, a KF titration cell installed into a general-purpose titrator. There are also oven attachments that can be used for materials that have problems being analyzed normally in the cell. The important aspect about the oven attachment is that the material doesn't decompose into water when heated to release the water. The oven attachment also supports automation of samples.
Using volumetric titration with visual detection of a titration endpoint is also possible with coloured samples by UV/VIS spectrophotometric detection. [ 4 ] | https://en.wikipedia.org/wiki/Karl_Fischer_titration |
Karl Küpfmüller (6 October 1897 – 26 December 1977) was a German electrical engineer, who was prolific in the areas of communications technology, measurement and control engineering, acoustics, communication theory, and theoretical electro-technology.
Küpfmüller was born in Nuremberg , where he studied at the Ohm-Polytechnikum. After returning from military service in World War I , he worked at the telegraph research division of the German Post in Berlin as a co-worker of Karl Willy Wagner , and, from 1921, he was lead engineer at the central laboratory of Siemens & Halske AG in the same city.
In 1928 he became full professor of general and theoretical electrical engineering at the Technische Hochschule in Danzig , and later held the same position in Berlin. Küpfmüller joined the National Socialist Motor Corps in 1933. In the following year he also joined the SA . In 1937 Küpfmüller joined the NSDAP and became a member of the SS , where he reached the rank of Obersturmbannführer . [ 1 ]
Küpfmüller was appointed as director of communication technology Research & Development at the Siemens -Wernerwerk for telegraphy. In 1941–1945 he was director of the central R&D division at Siemens & Halske in 1937.
From 1952 until his retirement in 1963, he held the chair for general communications engineering at Technische Hochschule Darmstadt . [ 2 ] [ 3 ]
Later he was honorary professor at the Technische Hochschule Berlin . In 1968, he received the Werner von Siemens Ring for his contributions to the theory of telecommunications and other electro-technology.
He died at Darmstadt .
About 1928, he did the same analysis that Harry Nyquist did, to show that not more than 2B independent pulses per second could be put through a channel of bandwidth B. He did this by quantifying the time-bandwidth product k of various communication signal types, and showing that k could never be less than 1/2. [ 4 ] From his 1931 paper (rough translation from Swedish): [ 5 ] | https://en.wikipedia.org/wiki/Karl_Küpfmüller |
Karl Spencer Lashley (June 7, 1890 – August 7, 1958) was an American psychologist and behaviorist remembered for his contributions to the study of learning and memory. A Review of General Psychology survey, published in 2002, ranked Lashley as the 61st most cited psychologist of the 20th century. [ 1 ] [ 2 ]
Lashley was born on June 7, 1890, in the town of Davis, West Virginia . He was the only child of Charles and Maggie Lashley. He grew up in a middle-class family with a reasonably comfortable life. Lashley's father held various local political positions. His mother was a stay-at-home parent, and had a vast collection of books in the home. She brought in women from the community, whom she would teach various subjects. This is no doubt what gave Lashley his love of learning. Lashley has always held his family in high regard. He has said that his father was a kind man. [ citation needed ]
Lashley's mother was a strong advocate of schooling, and she encouraged Lashley intellectually from an early age. Lashley was a very active boy, both physically and mentally. He was able to read by the age of four. His favorite thing to do as a child was to wander through the woods and collect animals, like butterflies and mice. He spent most of his childhood alone. Lashley did not have many friends. The reasons for his lack of friendships is unclear. Lashley graduated high school at age 14.
Lashley enrolled at West Virginia University , where he had originally intended to become an English major. He took a course in zoology , however, and switched his major to zoology due to his interactions with the professor John Black Johnston. Lashley wrote, "Within a few weeks in his class I knew that I had found my life's work". [ 3 ]
After obtaining his Bachelor of Arts at West Virginia University, Lashley was awarded a teaching fellowship at the University of Pittsburgh , where he taught biology along with biological laboratories. While there he also carried out research which he used for his master's thesis. [ 4 ] Once Lashley completed his master's degree, he studied at Johns Hopkins University , where he received his PhD in genetics in June 1911. He became a professor at University of Minnesota , University of Chicago , and Harvard University .
At Hopkins, Lashley minored in psychology under John B. Watson , whom he continued to work closely with him after receiving his PhD. It was during this time that Lashley worked with Shepherd Ivory Franz and was introduced to his training/ablation method. Watson had a great deal of influence on Lashley. Together the two conducted field experiments and studied the effects of different drugs on maze learning of rats. [ 4 ] Watson helped Lashley to focus on specific problems in learning and experimental investigation, followed by locating the area of the cerebrum involved in learning and discrimination.
Lashley's career began with research concerning brain mechanisms and how they were related to sense receptors. He also conducted work on instinct as well as color vision. He studied many animals and primates, which had been an interest since his freshman year at college.
Lashley worked at the University of Minnesota from 1917 to 1926 and then at the Institute for Juvenile Research in Chicago before becoming a professor at the University of Chicago . After this he went to Harvard , but was dissatisfied and from there became the director of the Yerkes Laboratory of Primate Biology in Orange Park, Florida.
Lashley's most influential research centered around the cortical basis of learning and discrimination. He researched this by looking at the measurement of behavior before and after specific, carefully quantified, induced brain damage in rats. Lashley trained rats to perform specific tasks (seeking a food reward), then lesioned specific areas of the rats' cortex, either before or after the animals received the training. The cortical lesions had specific effects on acquisition and retention of knowledge, but the location of the removed cortex had no effect on the rats' performance in the maze. This led Lashley to conclude that memories are not localized, but that they are widely distributed across the cortex. Today we know that distribution of engrams does in fact exist, but that the distribution is not equal across all cortical areas, as Lashley assumed. [ 5 ] [ 6 ] His study of V1 (primary visual cortex) led him to believe that it was a site of learning and memory storage (i.e. an engram) in the brain. He reached this erroneous conclusion due to imperfect lesioning methods.
By the 1950s, two separate principles had grown out of Lashley's research: mass action and equipotentiality . "Mass action" refers to the idea that the rate, efficacy and accuracy of learning depend on the amount of cortex available. If cortical tissue is destroyed following the learning of a complex task, deterioration of performance on the task is determined more by the amount of tissue destroyed than by its location. [ 7 ] "Equipotentiality" refers to the idea that one part of the cortex can take over the function of another part; within a functional area of the brain, any tissue within that area can perform its associated function. [ 8 ] Therefore, to destroy a function, all the tissue within a functional area must be destroyed. If the area is not destroyed then the cortex can take over another part. These two principles grew out of Lashley's research on the cortical basis of learning and discrimination.
In February 1954, while doing his teaching at Harvard, Lashley unexpectedly collapsed and was hospitalized. He was diagnosed with hemolytic anemia and put on a cortisone treatment. This eventually began to soften his vertebrae, and as a result a splenectomy was performed. Lashley was on the road to a full recovery until his trip to France with his wife Clair, where he once again unexpectedly collapsed, but this time to his death on August 7, 1958. [ 4 ]
Lashley was elected to many scientific and philosophical societies, including the American Psychological Association (Council member 1926–1928; President, 1929), Eastern Psychological Association (President, 1937), Society of Experimental Psychologists, British Psychological Association (Honorary Fellow), American Society of Zoologists, American Society of Naturalists (President, 1947), British Institute for the Study of Animal Behavior (Honorary Member), American Society of Human Genetics, American Physiological Society, Harvey Society (Honorary Member), National Academy of Sciences (elected in 1930). [ 4 ] In 1938, Lashley was elected a Member of the American Philosophical Society , the oldest learned society in the United States, dating to 1743. Since 1957, the Society has awarded the annual Karl Spencer Lashley Award in recognition of work on the integrative neuroscience of behavior. [ 9 ] In 1943, Lashley was awarded the Daniel Giraud Elliot Medal from the National Academy of Sciences . [ 10 ]
Lashley was awarded honorary Doctor of Science degrees from the University of Pittsburgh (1936), the University of Chicago (1941), Western Reserve University (1951), the University of Pennsylvania ; in 1953, Johns Hopkins University presented him with an honorary Doctor of Laws degree. [ 4 ]
Lashley had a reputation as an objective scientist, but Nadine Weidman has tried to expose him as racist and a genetic determinist. However, Donald Dewsbury and others have disputed the claim that he was a genetic determinist, citing research of Lashley's in which he found evidence of both genetic and environmental influences on organisms. Dewsbury does admit, however, that Lashley was quite racist. He cites a line from a letter that Lashley wrote to a German colleague which reads: "Too bad that the beautiful tropical countries are all populated by negros. Heil Hitler and Apartheit!" [ 11 ] This line alone would leave little debate on this matter, but he cites others as well. | https://en.wikipedia.org/wiki/Karl_Lashley |
Sir Karl Raimund Popper CH FRS FBA [ 4 ] (28 July 1902 – 17 September 1994) was an Austrian–British [ 5 ] philosopher, academic and social commentator . [ 6 ] [ 7 ] [ 8 ] One of the 20th century's most influential philosophers of science , [ 9 ] [ 10 ] [ 11 ] Popper is known for his rejection of the classical inductivist views on the scientific method in favour of empirical falsification , and for founding the LSE's Department of Philosophy. [ 12 ] According to Popper, a theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can (and should) be scrutinised with decisive experiments. Popper was opposed to the classical justificationist account of knowledge, which he replaced with "the first non-justificational philosophy of criticism in the history of philosophy", namely critical rationalism . [ 13 ]
In political discourse, he is known for his vigorous defence of liberal democracy and the principles of social criticism that he believed made a flourishing open society possible. His political thought resides within the camp of Enlightenment rationalism and humanism. He was a dogged opponent of totalitarianism, nationalism, fascism, romanticism, collectivism, and other kinds of (in Popper's view) reactionary and irrational ideas, and identified modern liberal democracies as the best-to-date embodiment of an open society . [ 3 ]
Karl Popper was born in Vienna (then in Austria-Hungary ) in 1902 to upper-middle-class parents. All of Popper's grandparents were assimilated Jews ; the Popper family converted to Lutheranism before he was born [ 14 ] [ 15 ] and so he received a Lutheran baptism. [ 16 ] [ 17 ] His father, Simon Siegmund Carl Popper (1856–1932), was a lawyer from Bohemia and a doctor of law at the Vienna University . His mother, Jenny Schiff (1864–1938), was an accomplished pianist of Silesian and Hungarian descent. Popper's uncle was the Austrian philosopher Josef Popper-Lynkeus . After establishing themselves in Vienna, the Poppers made a rapid social climb in Viennese society, as Popper's father became a partner in the law firm of Vienna's liberal mayor Raimund Grübl , and after Grübl's death in 1898 took over the business. Popper received his middle name after Raimund Grübl. [ 14 ] (In his autobiography, Popper erroneously recalls that Grübl's first name was Carl). [ 18 ] His parents were close friends of Sigmund Freud 's sister Rosa Graf. [ 19 ] His father was a bibliophile who had 12,000–14,000 volumes in his personal library [ 20 ] and took an interest in philosophy, the classics, and social and political issues. [ 9 ] Popper inherited both the library and the disposition from him. [ 21 ] Later, he would describe the atmosphere of his upbringing as having been "decidedly bookish". [ 9 ]
Popper left school at the age of 16 and attended lectures in mathematics, physics, philosophy, psychology and the history of music as a guest student at the University of Vienna. In 1919, Popper became attracted by Marxism and subsequently joined the Association of Socialist School Students. He also became a member of the Social Democratic Workers' Party of Austria , which was at that time a party that fully adopted Marxism. [ 9 ] After the street battle in the Hörlgasse on 15 June 1919, when police shot eight of his unarmed party comrades, he turned away from what he saw as the philosopher Karl Marx 's historical materialism , abandoned the ideology, and remained a supporter of social liberalism throughout his life. [ 3 ]
Popper worked in street construction for a short time but was unable to cope with the heavy labour. Continuing to attend university as a guest student, he started an apprenticeship as a cabinetmaker, which he completed as a journeyman. He was dreaming at that time of starting a daycare facility for children, for which he assumed the ability to make furniture might be useful. After that, he did voluntary service in one of psychoanalyst Alfred Adler 's clinics for children. In 1922, he did his matura by way of a second chance education and finally joined the university as an ordinary student. He completed his examination as an elementary teacher in 1924 and started working at an after-school care club for socially endangered children. In 1925, he went to the newly founded Pädagogisches Institut and continued studying philosophy and psychology. Around that time he started courting Josefine Anna Henninger, who later became his wife.
Popper and his wife had chosen not to have children because of the circumstances of war in the early years of their marriage. Popper commented that this "was perhaps a cowardly but in a way a right decision". [ 22 ]
In 1928, Popper earned a doctorate in psychology, under the supervision of Karl Bühler —with Moritz Schlick being the second chair of the thesis committee . His dissertation was titled Zur Methodenfrage der Denkpsychologie ( On Questions of Method in the Psychology of Thinking ). [ 23 ] In 1929, he obtained an authorisation to teach mathematics and physics in secondary school and began doing so. He married his colleague Josefine Anna Henninger (1906–1985) in 1930. Fearing the rise of Nazism and the threat of the Anschluss , he started to use the evenings and the nights to write his first book Die beiden Grundprobleme der Erkenntnistheorie ( The Two Fundamental Problems of the Theory of Knowledge ). He needed to publish a book to get an academic position in a country that was safe for people of Jewish descent. In the end, he did not publish the two-volume work; but instead, a condensed version with some new material, as Logik der Forschung ( The Logic of Scientific Discovery ) in 1934. Here, he criticised psychologism , naturalism , inductivism , and logical positivism , and put forth his theory of potential falsifiability as the criterion demarcating science from non-science. In 1935 and 1936, he took unpaid leave to go to the United Kingdom for a study visit. [ 24 ]
In 1937, Popper finally managed to get a position that allowed him to emigrate to New Zealand, where he became lecturer in philosophy at Canterbury University College of the University of New Zealand in Christchurch . It was here that he wrote his influential work The Open Society and Its Enemies . In Dunedin he met the Professor of Physiology John Carew Eccles and formed a lifelong friendship with him. In 1946, after the Second World War , he moved to the United Kingdom to become a reader in logic and scientific method at the London School of Economics (LSE), a constituent School of the University of London , where, three years later, in 1949, he was appointed professor of logic and scientific method. Popper was president of the Aristotelian Society from 1958 to 1959. He resided in Penn, Buckinghamshire . [ 25 ]
Popper retired from academic life in 1969, though he remained intellectually active for the rest of his life. In 1985, he returned to Austria so that his wife could have her relatives around her during the last months of her life; she died in November that year. After the Ludwig Boltzmann Gesellschaft failed to establish him as the director of a newly founded branch researching the philosophy of science, he went back again to the United Kingdom in 1986, settling in Kenley , Surrey. [ 4 ]
Popper died of "complications of cancer , pneumonia and kidney failure " in Kenley at the age of 92 on 17 September 1994. [ 26 ] [ 27 ] He had been working continuously on his philosophy until two weeks before when he suddenly fell terminally ill, writing his last letter two weeks before his death as well. [ 28 ] [ 29 ]
After cremation, his ashes were taken to Vienna and buried at Lainzer cemetery adjacent to the ORF Centre, where his wife Josefine Anna Popper (called "Hennie") had already been buried. Popper's estate is managed by his secretary and personal assistant Melitta Mew and her husband Raymond. Popper's manuscripts went to the Hoover Institution at Stanford University , partly during his lifetime and partly as supplementary material after his death. The University of Klagenfurt acquired Popper's library in 1995. The Karl Popper Archives was established within the Klagenfurt University Library, holding Popper's library of approximately 6,000 books, including his precious bibliophilia, as well as hard copies of the original Hoover material and microfilms of the incremental material. [ 30 ] The library as well as various other partial collections are open for researcher purposes. The remaining parts of the estate were mostly transferred to The Karl Popper Charitable Trust. [ 31 ] In October 2008, the University of Klagenfurt acquired the copyrights from the estate.
Popper won many awards and honours in his field, including the Lippincott Award of the American Political Science Association , the Sonning Prize , the Otto Hahn Peace Medal of the United Nations Association of Germany in Berlin and fellowships in the Royal Society, [ 4 ] British Academy , London School of Economics , King's College London , Darwin College , Cambridge , Austrian Academy of Sciences and Charles University, Prague . Austria awarded him the Grand Decoration of Honour in Gold for Services to the Republic of Austria in 1986, and the Federal Republic of Germany its Grand Cross with Star and Sash of the Order of Merit , and the peace class of the Order Pour le Mérite . He was knighted by Queen Elizabeth II in 1965, [ 32 ] and was elected a Fellow of the Royal Society in 1976. [ 4 ] He was invested with the insignia of a Member of the Order of the Companions of Honour in 1982. [ 33 ]
Other awards and recognition for Popper included the City of Vienna Prize for the Humanities (1965), Karl Renner Prize (1978), Austrian Decoration for Science and Art (1980), Dr. Leopold Lucas Prize of the University of Tübingen (1980), Ring of Honour of the City of Vienna (1983) and the Premio Internazionale of the Italian Federico Nietzsche Society (1988). In 1989, he was the first awarded the Prize International Catalonia for "his work to develop cultural, scientific and human values all around the world". [ 34 ] In 1992, he was awarded the Kyoto Prize in Arts and Philosophy for "symbolising the open spirit of the 20th century" [ 35 ] and for his "enormous influence on the formation of the modern intellectual climate". [ 35 ]
Popper's rejection of Marxism during his teenage years left a profound mark on his thought. He had at one point joined a socialist association, and for a few months in 1919 considered himself a communist . [ 36 ] Although it is known that Popper worked as an office boy at the communist headquarters, whether or not he ever became a member of the Communist Party is unclear. [ 37 ] During this time he became familiar with the Marxist view of economics, class conflict , and history. [ 9 ] Although he quickly became disillusioned with the views expounded by Marxists, his flirtation with the ideology led him to distance himself from those who believed that spilling blood for the sake of a revolution was necessary. He then took the view that when it came to sacrificing human lives, one was to think and act with extreme prudence.
The failure of democratic parties to prevent fascism from taking over Austrian politics in the 1920s and 1930s traumatised Popper. He suffered from the direct consequences of this failure since events after the Anschluss (the annexation of Austria by the German Reich in 1938) forced him into permanent exile. His most important works in the field of social science — The Poverty of Historicism (1944) and The Open Society and Its Enemies (1945)—were inspired by his reflection on the events of his time and represented, in a sense, a reaction to the prevalent totalitarian ideologies that then dominated Central European politics. His books defended democratic liberalism as a social and political philosophy . They also represented extensive critiques of the philosophical presuppositions underpinning all forms of totalitarianism . [ 9 ]
Popper believed that there was a contrast between the theories of Sigmund Freud and Alfred Adler , which he considered non-scientific, and Albert Einstein 's theory of relativity which set off the revolution in physics in the early 20th century. Popper thought that Einstein's theory, as a theory properly grounded in scientific thought and method, was highly "risky", in the sense that it was possible to deduce consequences from it which differed considerably from those of the then-dominant Newtonian physics ; one such prediction, that gravity could deflect light, was verified by Eddington's experiments in 1919 . [ 38 ] In contrast he thought that nothing could, even in principle, falsify psychoanalytic theories. He thus came to the conclusion that they had more in common with primitive myths than with genuine science. [ 9 ]
This led Popper to conclude that what was regarded as the remarkable strengths of psychoanalytical theories were actually their weaknesses. Psychoanalytical theories were crafted in a way that made them able to refute any criticism and to give an explanation for every possible form of human behaviour. The nature of such theories made it impossible for any criticism or experiment—even in principle—to show them to be false. [ 9 ] When Popper later tackled the problem of demarcation in the philosophy of science, this conclusion led him to posit that the strength of a scientific theory lies in its both being susceptible to falsification, and not actually being falsified by criticism made of it. He considered that if a theory cannot, in principle, be falsified by criticism, it is not a scientific theory. [ 39 ]
Popper coined the term "critical rationalism" to describe his philosophy. [ 40 ] Popper rejected the empiricist view (following from Kant) that basic statements are infallible; rather, according to Popper, they are descriptions in relation to a theoretical framework. [ 41 ] Concerning the method of science, the term "critical rationalism" indicates his rejection of classical empiricism , and the classical observationalist-inductivist account of science that had grown out of it. [ 42 ] Popper argued strongly against the latter, holding that scientific theories are abstract in nature and can be tested only indirectly, by reference to their implications. [ 43 ] He also held that scientific theory, and human knowledge generally, is irreducibly conjectural or hypothetical, and is generated by the creative imagination to solve problems that have arisen in specific historico-cultural settings.
Logically, no number of positive outcomes at the level of experimental testing can confirm a scientific theory, but a single counterexample is logically decisive; it shows the theory, from which the implication is derived, to be false. Popper's account of the logical asymmetry between verification and falsifiability lies at the heart of his philosophy of science. It also inspired him to take falsifiability as his criterion of demarcation between metaphysics and science: a theory should be considered scientific if, and only if, it makes predictions that can be falsified. This led him to attack the claims of both psychoanalysis and contemporary Marxism to scientific status, on the basis that it is not possible to falsify the predictions that they make.
To say that a given statement (e.g., the statement of a law of some scientific theory)—call it "T"—is " falsifiable " does not mean that "T" is false. It means only that the background knowledge about existing technologies, which exists before and independently of the theory, allows the imagination or conceptualization of observations that are in contradiction with the theory. It is only required that these contradictory observations can potentially be observed with existing technologies—the observations must be inter-subjective. This is the material requirement of falsifiability. Alan Chalmers gives "The brick fell upward when released" as an example of an imaginary observation that shows that Newton's law of gravitation is falsifiable. [ 44 ]
In All Life is Problem Solving , Popper sought to explain the apparent progress of scientific knowledge—that is, how it is that our understanding of the universe seems to improve over time. This problem arises from his position that the truth content of our theories, even the best of them, cannot be verified by scientific testing, but can only be falsified. With only falsifications being possible logically, how can we explain the growth of knowledge ? In Popper's view, the advance of scientific knowledge is an evolutionary process characterised by his formula: [ 45 ] [ 46 ]
P S 1 → T T 1 → E E 1 → P S 2 . {\displaystyle \mathrm {PS} _{1}\rightarrow \mathrm {TT} _{1}\rightarrow \mathrm {EE} _{1}\rightarrow \mathrm {PS} _{2}.\,}
In response to a given problem situation ( P S 1 {\displaystyle \mathrm {PS} _{1}} ), a number of competing conjectures, or tentative theories ( T T {\displaystyle \mathrm {TT} } ), are systematically subjected to the most rigorous attempts at falsification possible. This process, error elimination ( E E {\displaystyle \mathrm {EE} } ), performs a similar function for science that natural selection performs for biological evolution . Theories that better survive the process of refutation are not more true, but rather, more "fit"—in other words, more applicable to the problem situation at hand ( P S 1 {\displaystyle \mathrm {PS} _{1}} ). Consequently, just as a species' biological fitness does not ensure continued survival, neither does rigorous testing protect a scientific theory from refutation in the future. Yet, as it appears that the engine of biological evolution has, over many generations, produced adaptive traits equipped to deal with more and more complex problems of survival, likewise, the evolution of theories through the scientific method may, in Popper's view, reflect a certain type of progress: toward more and more interesting problems ( P S 2 {\displaystyle \mathrm {PS} _{2}} ). For Popper, it is in the interplay between the tentative theories (conjectures) and error elimination (refutation) that scientific knowledge advances toward greater and greater problems; in a process very much akin to the interplay between genetic variation and natural selection.
Popper also wrote extensively against the famous Copenhagen interpretation of quantum mechanics . He strongly disagreed with Niels Bohr 's instrumentalism and supported Albert Einstein 's scientific realist approach to scientific theories about the universe. He found that Bohr's interpretation introduced subjectivity into physics, claiming later in his life that:
Bohr was "a marvelous physicist, one of the greatest of all time, but he was a miserable philosopher, and one couldn't talk to him. He was talking all the time, allowing practically only one or two words to you and then at once cutting in." [ 47 ]
This Popper's falsifiability resembles Charles Peirce 's nineteenth-century fallibilism . In Of Clocks and Clouds (1966), Popper remarked that he wished he had known of Peirce's work earlier.
Among his contributions to philosophy is his claim to have solved the philosophical problem of induction . He states that while there is no way to prove that the sun will rise, it is possible to formulate the theory that every day the sun will rise; if it does not rise on some particular day, the theory will be falsified and will have to be replaced by a different one. Until that day, there is no need to reject the assumption that the theory is true. Nor is it rational according to Popper to make instead the more complex assumption that the sun will rise until a given day, but will stop doing so the day after, or similar statements with additional conditions. Such a theory would be true with higher probability because it cannot be attacked so easily:
Popper held that it is the least likely, or most easily falsifiable, or simplest theory (attributes which he identified as all the same thing) that explains known facts that one should rationally prefer. His opposition to positivism, which held that it is the theory most likely to be true that one should prefer, here becomes very apparent. It is impossible, Popper argues, to ensure a theory to be true; it is more important that its falsity can be detected as easily as possible.
Popper agreed with David Hume that there is often a psychological belief that the sun will rise tomorrow and that there is no logical justification for the supposition that it will, simply because it always has in the past. Popper writes,
I approached the problem of induction through Hume. Hume, I felt, was perfectly right in pointing out that induction cannot be logically justified. [ 48 ]
Popper held that rationality is not restricted to the realm of empirical or scientific theories, but that it is merely a special case of the general method of criticism, the method of finding and eliminating contradictions in knowledge without ad-hoc measures. According to this view, rational discussion about metaphysical ideas, about moral values and even about purposes is possible. Popper's student W.W. Bartley III tried to radicalise this idea and made the controversial claim that not only can criticism go beyond empirical knowledge but that everything can be rationally criticised.
To Popper, who was an anti- justificationist , traditional philosophy is misled by the false principle of sufficient reason . He thinks that no assumption can ever be or needs ever to be justified, so a lack of justification is not a justification for doubt. Instead, theories should be tested and scrutinised. It is not the goal to bless theories with claims of certainty or justification, but to eliminate errors in them. He writes,
[T]here are no such things as good positive reasons; nor do we need such things [...] But [philosophers] obviously cannot quite bring [themselves] to believe that this is my opinion, let alone that it is right. ( The Philosophy of Karl Popper , p. 1043)
Popper's principle of falsifiability runs into prima facie difficulties when the epistemological status of mathematics is considered. It is difficult to conceive how simple statements of arithmetic, such as "2 + 2 = 4", could ever be shown to be false. If they are not open to falsification they can not be scientific. If they are not scientific, it needs to be explained how they can be informative about real world objects and events.
Popper's solution [ 49 ] was an original contribution in the philosophy of mathematics . His idea was that a number statement such as "2 apples + 2 apples = 4 apples" can be taken in two senses. In its pure mathematics sense, "2 + 2 = 4" is logically true and cannot be refuted. Contrastingly, in its applied mathematics sense of it describing the physical behaviour of apples, it can be falsified. This can be done by placing two apples in a container, then proceeding to place another two apples in the same container. If there are five, three, or a number of apples that is not four in said container, the theory that "2 apples + 2 apples = 4 apples" is shown to be false. On the contrary, if there are four apples in the container, the theory of numbers is shown to be applicable to reality. [ 50 ]
In The Open Society and Its Enemies and The Poverty of Historicism , Popper developed a critique of historicism and a defence of the "Open Society". Popper considered historicism to be the theory that history develops inexorably and necessarily according to knowable general laws towards a determinate end. He argued that this view is the principal theoretical presupposition underpinning most forms of authoritarianism and totalitarianism . He argued that historicism is founded upon mistaken assumptions regarding the nature of scientific law and prediction. Since the growth of human knowledge is a causal factor in the evolution of human history, and since "no society can predict, scientifically, its own future states of knowledge", [ 51 ] it follows, he argued, that there can be no predictive science of human history. For Popper, metaphysical and historical indeterminism go hand in hand.
In his early years Popper was impressed by Marxism, whether of Communists or socialists. An event that happened in 1919 had a profound effect on him: During a riot, caused by the Communists, the police shot several unarmed people, including some of Popper's friends, when they tried to free party comrades from prison. The riot had, in fact, been part of a plan by which leaders of the Communist party with connections to Béla Kun tried to take power by a coup; Popper did not know about this at that time. However, he knew that the riot instigators were swayed by the Marxist doctrine that class struggle would produce vastly more dead men than the inevitable revolution brought about as quickly as possible, and so had no scruples to put the life of the rioters at risk to achieve their selfish goal of becoming the future leaders of the working class. This was the start of his later criticism of historicism. [ 52 ] [ 53 ] Popper began to reject Marxist historicism, which he associated with questionable means, and later socialism , which he associated with placing equality before freedom (to the possible disadvantage of equality). [ 54 ]
Popper said that he was a socialist for "several years", and maintained an interest in egalitarianism, [ 55 ] but abandoned it as a whole because socialism was a "beautiful dream", but, just like egalitarianism, it was incompatible with individual liberty. [ 56 ] Popper initially saw totalitarianism as exclusively right-wing in nature, [ 55 ] although as early as 1945 in The Open Society he was describing Communist parties as giving a weak opposition to fascism due to shared historicism with fascism. [ 57 ] : 730 [ 58 ] Over time, primarily in defence of liberal democracy, Popper began to see Soviet-type communism as a form of totalitarianism, [ 55 ] and viewed the main issue of the Cold War as not capitalism versus socialism, but democracy versus totalitarianism. [ 57 ] : 732 In 1957, Popper would dedicate The Poverty of Historicism to "memory of the countless men, women and children of all creeds or nations or races who fell victims to the fascist and communist belief in Inexorable Laws of Historical Destiny." [ 55 ]
In 1947, Popper co-founded the Mont Pelerin Society , with Friedrich Hayek , Milton Friedman , Ludwig von Mises and others, although he did not fully agree with the think tank's charter and ideology. Specifically, he unsuccessfully recommended that socialists should be invited to participate, and that emphasis should be put on a hierarchy of humanitarian values rather than advocacy of a free market as envisioned by classical liberalism . [ 59 ]
Although Popper was an advocate of toleration, he also warned against unlimited tolerance. In The Open Society and Its Enemies , he argued:
Unlimited tolerance must lead to the disappearance of tolerance. If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them. In this formulation, I do not imply, for instance, that we should always suppress the utterance of intolerant philosophies; as long as we can counter them by rational argument and keep them in check by public opinion, suppression would certainly be most unwise. But we should claim the right to suppress them if necessary even by force; for it may easily turn out that they are not prepared to meet us on the level of rational argument, but begin by denouncing all argument; they may forbid their followers to listen to rational argument, because it is deceptive, and teach them to answer arguments by the use of their fists or pistols. We should therefore claim, in the name of tolerance, the right not to tolerate the intolerant. We should claim that any movement preaching intolerance places itself outside the law, and we should consider incitement to intolerance and persecution as criminal, in the same way as we should consider incitement to murder, or to kidnapping, or to the revival of the slave trade, as criminal. [ 60 ] [ 61 ] [ 62 ] [ 63 ]
Popper criticized what he termed the "conspiracy theory of society", the view that powerful people or groups, godlike in their efficacy, are responsible for purposely bringing about all the ills of society. This view cannot be right, Popper argued, because "nothing ever comes off exactly as intended." [ 64 ] According to philosopher David Coady, "Popper has often been cited by critics of conspiracy theories, and his views on the topic continue to constitute an orthodoxy in some circles." [ 65 ] However, philosopher Charles Pigden has pointed out that Popper's argument only applies to a very extreme kind of conspiracy theory, not to conspiracy theories generally. [ 66 ]
As early as 1934, Popper wrote of the search for truth as "one of the strongest motives for scientific discovery." [ 67 ] Still, he describes in Objective Knowledge (1972) early concerns about the much-criticised notion of truth as correspondence . Then came the semantic theory of truth formulated by the logician Alfred Tarski and published in 1933. Popper wrote of learning in 1935 of the consequences of Tarski's theory, to his intense joy. The theory met critical objections to truth as correspondence and thereby rehabilitated it. The theory also seemed, in Popper's eyes, to support metaphysical realism and the regulative idea of a search for truth.
According to this theory, the conditions for the truth of a sentence as well as the sentences themselves are part of a metalanguage . So, for example, the sentence "Snow is white" is true if and only if snow is white. Although many philosophers have interpreted, and continue to interpret, Tarski's theory as a deflationary theory , Popper refers to it as a theory in which "is true" is replaced with " corresponds to the facts ". He bases this interpretation on the fact that examples such as the one described above refer to two things: assertions and the facts to which they refer. He identifies Tarski's formulation of the truth conditions of sentences as the introduction of a "metalinguistic predicate" and distinguishes the following cases:
The first case belongs to the metalanguage whereas the second is more likely to belong to the object language. Hence, "it is true that" possesses the logical status of a redundancy. "Is true", on the other hand, is a predicate necessary for making general observations such as "John was telling the truth about Phillip."
Upon this basis, along with that of the logical content of assertions (where logical content is inversely proportional to probability), Popper went on to develop his important notion of verisimilitude or "truthlikeness". The intuitive idea behind verisimilitude is that the assertions or hypotheses of scientific theories can be objectively measured with respect to the amount of truth and falsity that they imply. And, in this way, one theory can be evaluated as more or less true than another on a quantitative basis which, Popper emphasises forcefully, has nothing to do with "subjective probabilities" or other merely "epistemic" considerations.
The simplest mathematical formulation that Popper gives of this concept can be found in the tenth chapter of Conjectures and Refutations . Here he defines it as:
where V s ( a ) {\displaystyle {\mathit {Vs}}(a)} is the verisimilitude of a , C T v ( a ) {\displaystyle {\mathit {CT}}_{v}(a)} is a measure of the content of the truth of a , and C T f ( a ) {\displaystyle {\mathit {CT}}_{f}(a)} is a measure of the content of the falsity of a .
Popper's original attempt to define not just verisimilitude, but an actual measure of it, turned out to be inadequate. However, it inspired a wealth of new attempts. [ 9 ]
Knowledge, for Popper, was objective, both in the sense that it is objectively true (or truthlike), and also in the sense that knowledge has an ontological status (i.e., knowledge as object) independent of the knowing subject ( Objective Knowledge: An Evolutionary Approach , 1972). He proposed three worlds : [ 68 ] World One , being the physical world, or physical states; World Two , being the world of mind, or individuals' private mental states, ideas and perceptions; and World Three , being the public body of human knowledge expressed in its manifold forms (e.g., "scientific theories, ethical principles, characters in novels, philosophy, art, poetry, in short our entire cultural heritage" [ 69 ] ), or the products of World Two made manifest in the materials of World One (e.g., books, papers, paintings, symphonies, cathedrals, particle accelerators ). World Three, Popper argued, was the product of individual human beings in exactly the same sense that an animal path in the jungle is the creation of many individual animals but not planned or intended by any of them. World Three thus has an existence and an evolution independent of any individually known subjects. The influence of World Three on the individual human mind (World Two) is in Popper's view at least as strong as the influence of World One. In other words, the knowledge held by a given individual mind owes at least as much to the total, accumulated wealth of human knowledge made manifest as to the world of direct experience. As such, the growth of human knowledge could be said to be a function of the independent evolution of World Three.
Many contemporary philosophers, such as Daniel Dennett , [ 70 ] have not embraced Popper's Three World conjecture, mostly due to what they see as its resemblance to mind–body dualism . [ 71 ]
The creation–evolution controversy raised the issue of whether creationistic ideas may be legitimately called science. In the debate, both sides and even courts in their decisions have invoked Popper's criterion of falsifiability (see Daubert standard ). In this context, passages written by Popper are frequently quoted in which he speaks about such issues himself. For example, he famously stated " Darwinism is not a testable scientific theory, but a metaphysical research program—a possible framework for testable scientific theories." He continued:
And yet, the theory is invaluable. I do not see how, without it, our knowledge could have grown as it has done since Darwin. In trying to explain experiments with bacteria which become adapted to, say, penicillin , it is quite clear that we are greatly helped by the theory of natural selection . Although it is metaphysical, it sheds much light upon very concrete and very practical researches. It allows us to study adaptation to a new environment (such as a penicillin-infested environment) in a rational way: it suggests the existence of a mechanism of adaptation, and it allows us even to study in detail the mechanism at work. [ 72 ]
He noted that theism , presented as explaining adaptation, "was worse than an open admission of failure, for it created the impression that an ultimate explanation had been reached". [ 73 ] Popper later said:
When speaking here of Darwinism...This is an immensely impressive and powerful theory. The claim that it completely explains evolution is of course a bold claim, and very far from being established. All scientific theories are conjectures, even those that have successfully passed many severe and varied tests. The Mendelian underpinning of modern Darwinism has been well tested, and so has the theory of evolution.... [ 73 ]
He explained that the difficulty of testing had led some people to describe natural selection as a tautology , and that he too had in the past described the theory as "almost tautological", and had tried to explain how the theory could be untestable (as is a tautology) and yet of great scientific interest:
My solution was that the doctrine of natural selection is a most successful metaphysical research programme. It raises detailed problems in many fields, and it tells us what we would expect of an acceptable solution of these problems. I still believe that natural selection works in this way as a research programme. Nevertheless, I have changed my mind about the testability and logical status of the theory of natural selection; and I am glad to have an opportunity to make a recantation. [ 73 ]
Popper summarised his new view as follows:
The theory of natural selection may be so formulated that it is far from tautological. In this case it is not only testable, but it turns out to be not strictly universally true. There seem to be exceptions, as with so many biological theories; and considering the random character of the variations on which natural selection operates, the occurrence of exceptions is not surprising. Thus not all phenomena of evolution are explained by natural selection alone. Yet in every particular case it is a challenging research program to show how far natural selection can possibly be held responsible for the evolution of a particular organ or behavioural program. [ 74 ]
These frequently quoted passages are only a small part of what Popper wrote on evolution, however, and may give the wrong impression that he mainly discussed questions of its falsifiability. Popper never invented this criterion to give justifiable use of words like science. In fact, Popper stressed that "the last thing I wish to do, however, is to advocate another dogma" [ 75 ] and that "what is to be called a 'science' and who is to be called a 'scientist' must always remain a matter of convention or decision." [ 76 ] He quotes Menger's dictum that "Definitions are dogmas; only the conclusions drawn from them can afford us any new insight" [ 77 ] and notes that different definitions of science can be rationally debated and compared:
I do not try to justify [the aims of science which I have in mind], however, by representing them as the true or the essential aims of science. This would only distort the issue, and it would mean a relapse into positivist dogmatism. There is only one way, as far as I can see, of arguing rationally in support of my proposals. This is to analyse their logical consequences: to point out their fertility—their power to elucidate the problems of the theory of knowledge. [ 78 ]
Popper had his own sophisticated views on evolution [ 79 ] that go much beyond what the frequently-quoted passages say. [ 80 ] In effect, Popper agreed with some points of both creationists and naturalists, but disagreed with both on crucial aspects. Popper understood the universe as a creative entity that invents new things, including life, but without the necessity of something like a god, especially not one who is pulling strings from behind the curtain. He said that evolution of the genotype must, as the creationists say, work in a goal-directed way [ 81 ] but disagreed with their view that it must necessarily be the hand of god that imposes these goals onto the stage of life.
Instead, he formulated the spearhead model of evolution, a version of genetic pluralism. According to this, living organisms have goals, and act according to these goals, each guided by a central control. In its most sophisticated form, this is the brain of humans, but controls also exist in much less sophisticated ways for species of lower complexity, such as the amoeba . This control organ plays a special role in evolution—it is the "spearhead of evolution". The goals bring the purpose into the world. Mutations in the genes that determine the structure of the control may then cause drastic changes in behaviour, preferences and goals, without having an impact on the organism's phenotype . Popper postulates that such purely behavioural changes are less likely to be lethal for the organism compared to drastic changes of the phenotype. [ 82 ]
Popper contrasts his views with the notion of the "hopeful monster" that has large phenotype mutations and calls it the "hopeful behavioural monster". After behaviour has changed radically, small but quick changes of the phenotype follow to make the organism fitter to its changed goals. This way it looks as if the phenotype were changing guided by some invisible hand, while it is merely natural selection working in combination with the new behaviour. For example, according to this hypothesis, the eating habits of the giraffe must have changed before its elongated neck evolved. Popper contrasted this view as "evolution from within" or "active Darwinism" (the organism actively trying to discover new ways of life and being on a quest for conquering new ecological niches), [ 83 ] [ 84 ] with the naturalistic "evolution from without" (which has the picture of a hostile environment only trying to kill the mostly passive organism, or perhaps segregate some of its groups).
Popper was a key figure encouraging patent lawyer Günter Wächtershäuser to publish his iron–sulfur world hypothesis on abiogenesis and his criticism of "soup" theory .
On the creation-evolution controversy, Popper initially wrote that he considered it
a somewhat sensational clash between a brilliant scientific hypothesis concerning the history of the various species of animals and plants on earth, and an older metaphysical theory which, incidentally, happened to be part of an established religious belief
with a footnote to the effect that he
agree[s] with Professor C.E. Raven when...he calls this conflict 'a storm in a Victorian tea-cup'... [ 85 ]
In his later work, however, when he had developed his own "spearhead model" and "active Darwinism" theories, Popper revised this view and found some validity in the controversy:
I have to confess that this cup of tea has become, after all, my cup of tea; and with it I have to eat humble pie. [ 86 ]
Popper and John Eccles speculated on the problem of free will for many years, generally agreeing on an interactionist dualist theory of mind. However, although Popper was a body-mind dualist, he did not think that the mind is a substance separate from the body : he thought that mental or psychological properties or aspects of people are distinct from physical ones . [ 87 ]
When he gave the second Arthur Holly Compton Memorial Lecture in 1965, Popper revisited the idea of quantum indeterminacy as a source of human freedom. Eccles had suggested that "critically poised neurons" might be influenced by the mind to assist in a decision. Popper criticised Compton's idea of amplified quantum events affecting the decision. He wrote:
The idea that the only alternative to determinism is just sheer chance was taken over by Schlick , together with many of his views on the subject, from Hume , who asserted that "the removal" of what he called "physical necessity" must always result in "the same thing with chance . As objects must either be conjoin'd or not,... 'tis impossible to admit of any medium betwixt chance and an absolute necessity".
I shall later argue against this important doctrine according to which the alternative to determinism is sheer chance. Yet I must admit that the doctrine seems to hold good for the quantum-theoretical models which have been designed to explain, or at least to illustrate, the possibility of human freedom. This seems to be the reason why these models are so very unsatisfactory. [ 88 ]
Hume's and Schlick's ontological thesis that there cannot exist anything intermediate between chance and determinism seems to me not only highly dogmatic (not to say doctrinaire) but clearly absurd; and it is understandable only on the assumption that they believed in a complete determinism in which chance has no status except as a symptom of our ignorance. [ 89 ]
Popper called not for something between chance and necessity but for a combination of randomness and control to explain freedom, though not yet explicitly in two stages with random chance before the controlled decision, saying, "freedom is not just chance but, rather, the result of a subtle interplay between something almost random or haphazard, and something like a restrictive or selective control." [ 90 ]
Then in his 1977 book with John Eccles, The Self and its Brain , Popper finally formulates the two-stage model in a temporal sequence. And he compares free will to Darwinian evolution and natural selection:
New ideas have a striking similarity to genetic mutations. Now, let us look for a moment at genetic mutations. Mutations are, it seems, brought about by quantum theoretical indeterminacy (including radiation effects). Accordingly, they are also probabilistic and not in themselves originally selected or adequate, but on them there subsequently operates natural selection which eliminates inappropriate mutations. Now we could conceive of a similar process with respect to new ideas and to free-will decisions, and similar things.
That is to say, a range of possibilities is brought about by a probabilistic and quantum mechanically characterised set of proposals, as it were—of possibilities brought forward by the brain. On these there then operates a kind of selective procedure which eliminates those proposals and those possibilities which are not acceptable to the mind. [ 91 ]
Popper was not a religious man in the formal sense of the word. He neither maintained any link with his Jewish ancestry nor was he an observant Lutheran. However, he did consider that every person including himself, was religious in the sense of believing in something more important and beyond us through which we can transcend ourselves. Popper called this something a Third World . [ 92 ] In an interview that Popper gave in 1969 with the condition that it should be kept secret until after his death, he summarised his position on God as follows: "I don't know whether God exists or not (...) Some forms of atheism are arrogant and ignorant and should be rejected, but agnosticism —to admit that we don't know and to search—is all right. (...) When I look at what I call the gift of life, I feel a gratitude which is in tune with some religious ideas of God. However, the moment I even speak of it, I am embarrassed that I may do something wrong to God in talking about God." [ 93 ] [ 94 ] Aged fifteen, after reading Spinoza (at the suggestion of his father), Popper recounts that "it gave me a lifetime's dislike of theorizing about God". [ 95 ]
In 1936, applying to the Academic Assistance Council to leave Austria, he described himself as "Protestant, namely evangelical but of Jewish origin." Responding to the question of whether he wanted religious communities
approached on his behalf, opposite the Jewish Orthodox
section he wrote "NO", underlining it twice. [ 96 ]
Popper objected to organised religion, saying "it tends to use the name of God in vain", noting the danger of fanaticism because of religious conflicts: "The whole thing goes back to myths which, though they may have a kernel of truth, are untrue. Why then should the Jewish myth be true and the Indian and Egyptian myths not be true?" [ 93 ]
Ethical issues always constituted an important part of the background to Popper's philosophy. [ 97 ] In later life he discussed ethics rarely, and religious questions hardly at all, but he sympathized with the religious stance of others, and was not prepared to endorse various "humanist and secular offensives". [ 98 ] For Popper religion was definitely not science, but "because something isn’t science, however, does not mean it is meaningless". [ 93 ]
In a letter unrelated to the interview, he stressed his tolerant attitude: "Although I am not for religion, I do think that we should show respect for anybody who believes honestly." [ 4 ] [ 99 ] [ 100 ]
Popper helped to establish the philosophy of science as an autonomous discipline within philosophy, both through his own prolific and influential works and through his influence on his contemporaries and students. In 1946, Popper founded the Department of Philosophy, Logic and Scientific Method at the London School of Economics (LSE) and there lectured and influenced both Imre Lakatos and Paul Feyerabend , two of the foremost philosophers of science in the next generation. (Lakatos significantly modified Popper's position, [ 101 ] : 1 and Feyerabend repudiated it entirely, but the work of both was deeply influenced by Popper and engaged with many of the problems that Popper set.)
Although there is some dispute as to the matter of influence, Popper had a longstanding and close friendship with economist Friedrich Hayek , who was also brought to LSE from Vienna. Each found support and similarities in the other's work, citing each other often, though not without qualification. In a letter to Hayek in 1944, Popper stated, "I think I have learnt more from you than from any other living thinker, except perhaps Alfred Tarski ." [ 102 ] Popper dedicated his Conjectures and Refutations to Hayek. For his part, Hayek dedicated a collection of papers, Studies in Philosophy, Politics, and Economics , to Popper, and in 1982 said, "ever since his Logik der Forschung first came out in 1934, I have been a complete adherent to his general theory of methodology." [ 103 ]
Popper also had long and mutually influential friendships with art historian Ernst Gombrich , biologist Peter Medawar , and neuroscientist John Carew Eccles . The German jurist Reinhold Zippelius uses Popper's method of "trial and error" in his legal philosophy. [ 104 ] Peter Medawar called him "incomparably the greatest philosopher of science that has ever been". [ 105 ]
Popper's influence, both through his work in philosophy of science and through his political philosophy, has also extended beyond the academy. One of Popper's students at LSE was George Soros , who later became a billionaire investor and among whose philanthropic foundations is the Open Society Institute , a think-tank named in honour of Popper's The Open Society and Its Enemies . [ 106 ] [ 107 ] Soros revised his own philosophy, differing from some of Popper's epistemological assumptions, in a lecture entitled Open Society given at Central European University on 28 October 2009: [ 108 ]
Popper was mainly concerned with the problems of understanding of reality [...] He argued that and I quote "only democracy provides an institutional framework that permits reform without violence, and so the use of reason in politics matters." But his approach was based on a hidden assumption, namely, that the main purpose of thinking is to gain a better understanding of reality. And that was not necessarily the case. The manipulative function could take precedence over the cognitive function [...] How could Popper take it for granted that free political discourse is aimed at understanding reality? And even more intriguingly, how could I, who gave the manipulative function pride of place in the concept of reflexivity, follow him so blindly? [...] Let me spell out my conclusion more clearly, an open society is a desirable form of social organization, both as a means to an end, and an end in itself [...] provided it gives precedence to the cognitive over the manipulative function and people are willing to confront harsh realities. [...] The value of individual freedom is likely to assume increasing importance in the immediate future.
Most criticisms of Popper's philosophy are of the falsification , or error elimination, element in his account of problem solving. Popper presents falsifiability as both an ideal and as an important principle in a practical method of effective human problem solving; as such, the current conclusions of science are stronger than pseudo-sciences or non-sciences , insofar as they have survived this particularly vigorous selection method. [ 109 ]
He does not argue that any such conclusions are therefore true, or that this describes the actual methods of any particular scientist. Rather, it is recommended as an essential principle of methodology that, if enacted by a system or community, will lead to slow but steady progress of a sort (relative to how well the system or community enacts the method). It has been suggested that Popper's ideas are often mistaken for a hard logical account of truth because of the historical co-incidence of their appearing at the same time as logical positivism , the followers of which mistook his aims for their own. [ 110 ]
The Quine–Duhem thesis argues that it is impossible to test a single hypothesis on its own, since each one comes as part of an environment of theories. Thus we can only say that the whole package of relevant theories has been collectively falsified , but cannot conclusively say which element of the package must be replaced. An example of this is given by the discovery of the planet Neptune : when the motion of Uranus was found not to match the predictions of Newton's laws , the theory "There are seven planets in the solar system" was rejected, and not Newton's laws themselves. Popper discussed this critique of naive falsificationism in Chapters 3 and 4 of The Logic of Scientific Discovery .
The philosopher Thomas Kuhn writes in The Structure of Scientific Revolutions (1962) that he places an emphasis on anomalous experiences similar to that which Popper places on falsification. However, he adds that anomalous experiences cannot be identified with falsification, and questions whether theories could be falsified in the manner suggested by Popper. [ 111 ] Kuhn argues in The Essential Tension (1977) that while Popper was correct that psychoanalysis cannot be considered a science, there are better reasons for drawing that conclusion than those Popper provided. [ 112 ] Popper's student Imre Lakatos attempted to reconcile Kuhn's work with falsificationism by arguing that science progresses by the falsification of research programs rather than the more specific universal statements of naive falsificationism. [ 113 ]
Popper claimed to have recognised already in the 1934 version of his Logic of Discovery a fact later stressed by Kuhn, "that scientists necessarily develop their ideas within a definite theoretical framework", and to that extent to have anticipated Kuhn's central point about "normal science". [ 114 ] However, Popper criticised what he saw as Kuhn's relativism, this criticism being at the heart of the Kuhn-Popper debate . [ 115 ] Also, in his collection Conjectures and Refutations: The Growth of Scientific Knowledge (Harper & Row, 1963), Popper writes,
Science must begin with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices. The scientific tradition is distinguished from the pre-scientific tradition in having two layers. Like the latter, it passes on its theories; but it also passes on a critical attitude towards them. The theories are passed on, not as dogmas, but rather with the challenge to discuss them and improve upon them.
Another objection is that it is not always possible to demonstrate falsehood definitively, especially if one is using statistical criteria to evaluate a null hypothesis . More generally it is not always clear, if evidence contradicts a hypothesis, that this is a sign of flaws in the hypothesis rather than of flaws in the evidence. However, this is a misunderstanding of what Popper's philosophy of science sets out to do. Rather than offering a set of instructions that merely need to be followed diligently to achieve science, Popper makes it clear in The Logic of Scientific Discovery that his belief is that the resolution of conflicts between hypotheses and observations can only be a matter of the collective judgment of scientists, in each individual case. [ 116 ]
In Science Versus Crime , Houck writes [ 117 ] that Popper's falsificationism can be questioned logically: it is not clear how Popper would deal with a statement like "for every metal, there is a temperature at which it will melt". The hypothesis cannot be falsified by any possible observation, for there will always be a higher temperature than tested at which the metal may in fact melt, yet it seems to be a valid scientific hypothesis. These examples were pointed out by Carl Gustav Hempel . Hempel came to acknowledge that logical positivism's verificationism was untenable, but argued that falsificationism was equally untenable on logical grounds alone. The simplest response to this is that, because Popper describes how theories attain, maintain and lose scientific status, individual consequences of currently accepted scientific theories are scientific in the sense of being part of tentative scientific knowledge, and both of Hempel's examples fall under this category. For instance, atomic theory implies that all metals melt at some temperature.
An early adversary of Popper's critical rationalism, Karl-Otto Apel attempted a comprehensive refutation of Popper's philosophy. In Transformation der Philosophie (1973), Apel charged Popper with being guilty of, amongst other things, a pragmatic contradiction. [ 118 ]
The philosopher Adolf Grünbaum argues in The Foundations of Psychoanalysis (1984) that Popper's view that psychoanalytic theories, even in principle, cannot be falsified is incorrect. [ 119 ] The philosopher Roger Scruton argues in Sexual Desire (1986) that Popper was mistaken to claim that Freudian theory implies no testable observation and therefore does not have genuine predictive power. Scruton maintains that Freudian theory has both "theoretical terms" and "empirical content". He points to the example of Freud's theory of repression , which in his view has "strong empirical content" and implies testable consequences. Nevertheless, Scruton also concluded that Freudian theory is not genuinely scientific. [ 120 ] The philosopher Charles Taylor accuses Popper of exploiting his worldwide fame as an epistemologist to diminish the importance of philosophers of the 20th-century continental tradition . According to Taylor, Popper's criticisms are completely baseless, but they are received with an attention and respect that Popper's "intrinsic worth hardly merits". [ 121 ]
The philosopher John Gray argues that Popper's account of scientific method would have prevented the theories of Charles Darwin and Albert Einstein from being accepted. [ 122 ] However, Gray's criticism with regards to Einstein is at odds with the fact that Popper frequently used Einstein's theory of general relativity as a case study of how the principle of falsifiability works in practice. [ 123 ]
The philosopher and psychologist Michel ter Hark writes in Popper, Otto Selz and the Rise of Evolutionary Epistemology (2004) that Popper took some of his ideas from his tutor, the German psychologist Otto Selz . Selz never published his ideas, partly because of the rise of Nazism , which forced him to quit his work in 1933 and prohibited any reference to his ideas. Popper, the historian of ideas and his scholarship, is criticised in some academic quarters for his treatment of Plato and Hegel. [ 124 ] [ 125 ]
A complete list of Popper’s writings is available as part 1.1 of the International personal bibliography of Karl R. Popper on the website of Karl Popper Archives at the University of Klagenfurt (see also External links ). | https://en.wikipedia.org/wiki/Karl_Popper |
Karl Schlögl (October 5, 1924 – May 4, 2007) was professor of organic chemistry at the University of Vienna and secretary as well as vice-president of the Austrian Academy of Sciences .
Schlögl was born October 5, 1924, in Vienna . Schlögl's first contact with organic chemistry happened during his middle-school education, when his father - the principal and teacher for natural sciences - took young Karl to school after hours to do experiments together. [ 1 ] Schlögl graduated from high-school in 1943 and was declared unfit for service by the Wehrmacht due to his asthma .
He started studying chemistry at the University of Vienna under Ernst Späth , where he completed his dissertation in 1950.
From 1954 to 1955 Schlögl began working on ferrocenes at the University of Manchester during a British council scholarship .
After his return to the University of Vienna he achieved the habilitation for organic chemistry in 1959.
In 1970 Schlögl was promoted to associate professor and in 1971 to full professor for organic chemistry . [ 2 ]
Since 1974 he was director, and since 1978 chairman of the Institute of Organic Chemistry at the University of Vienna . From 1977 through 1979 he was the first elected Dean of the Faculty of Formal and Natural Sciences at the University of Vienna .
The Austrian Academy of Sciences elected Schlögl as a corresponding member in 1978 and as a full member in 1982. [ 3 ] From 1991 to 1995 Schlögl was general secretary of the academy, and from 1997 to 2000 he was vice-president of the Austrian Academy of Sciences . Furthermore, Schlögl was a corresponding member of the Nordrhein-Westfälische Akademie der Wissenschaften as well as the New York Academy of Sciences .
Schlögl was one of the pioneers of the research into the geometric structure of organic compounds and the resulting mechanisms of their chemical reactions. He has been very successful with his work on new pharmaceutical substances. [ 4 ]
Schlögl authored and co-authored over 200 scientific publications and was an inventor on four patents. [ 1 ] He supervised 51 dissertations of his doctoral students.
Schlögl's main field of research since about 1963 was stereochemistry , and in 1970 he began to shift his focus specifically on the chirality of organic compounds.
Schlögl received numerous scientific awards for his work, including the Erwin Schrödinger Prize of the Austrian Academy of Sciences in 1985, [ 5 ] the prize for natural sciences of the city of Vienna in 1989, and the Wilhelm Exner Medal of the Austrian Economic Association in 1991. [ 6 ] | https://en.wikipedia.org/wiki/Karl_Schlögl |
The Karl Schwarzschild Medal , named after the astrophysicist Karl Schwarzschild , is an award presented by the Astronomische Gesellschaft (German Astronomical Society) to eminent astronomers and astrophysicists. [ 1 ] [ 2 ]
Source: German Astronomical Society | https://en.wikipedia.org/wiki/Karl_Schwarzschild_Medal |
Karl Söllner (9 January 1903 – 14 June 1986) was an Austrian-American chemist, primarily active in the field of physical chemistry and biophysics .
Söllner was the son of lawyer Anton Maria Söllner and his wife Julie ( née Karplus). He grew up in Vienna and began studying chemistry and philosophy at the University of Vienna in 1921. From his third semester he was a student assistant (Demonstrator) at the university. He completed his dissertation with Alfons Klemenc. In 1928 he entered the service of the Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry in Berlin, where he worked as a scientific assistant alongside Herbert Freundlich . In May 1933, Söllner began a habilitation thesis in the field of osmosis which was reviewed by Fritz Haber , Max Bodenstein and Herbert Freundlich.
Unfortunately, in the same year the Nazi party seized power. According to the national socialist definition he was of Jewish heritage and was therefore forced him to leave his position at the institute in June 1933. He then emigrated to Great Britain, where he found a position in the chemistry department of University College London , where he worked from 1933 to 1937. He was also a visiting researcher and consultant at Imperial Chemical Industries .
In 1937 Söllner moved to the United States. There he took a position as a chemist with the Department of Agronomy at Cornell University in Ithaca with support from the “Emergency Committee in Aid of Displaced German Scholars“. In 1938 he moved to the Department of Physiological Chemistry at the University of Minnesota School of Medicine in Minneapolis . There he was initially employed as an Associate Chemist. He was promoted to "Regular Chemist" in 1939, Associate Professor in 1943 and Full Professor in 1947.
Söllner was labelled as an enemy of the state by Nazi authorities. In the spring of 1940, the Reich Security Main Office in Berlin put him on a special Great Britain wanted list , a list of people who, in the event of a successful invasion and occupation of the British Isles by the Wehrmacht, should be identified and arrested as a priority by the SS special forces that followed the occupation forces.
Later Söllner moved to the Institute of Health in Bethesda, Maryland where he worked in the laboratory of National Institute of Arthritis Metabolism and Digestive Diseases , initially at the rank of Principal Research Analyst, from 1948 as a senior physical biochemist and from 1965 as head of the section for electrochemistry and colloid chemistry . In 1973 he officially retired, but continued to work as a consultant and visiting researcher for the institute until 1975.
Söllner was a specialist in ultrasound for colloid systems. In this context, he focused his research on the study of membranes and their electrophysical properties and on "Studies of Dispersion of Solids, Coagulation, and Fog Formation". Söllner published about 120 scientific papers in specialist journals. He was also a member of the American Association for the Advancement of Science , the American Institute of Chemistry and the New York Academy of Sciences , the American Chemical Society , the Society of General Physiologists and the Electrochemical Society .
Söllner married Herta (Helen) Rosenberg on July 23, 1934. Their daughter Barbara Sollner-Webb embarked on a scientific career. | https://en.wikipedia.org/wiki/Karl_Söllner |
In combustion , the Karlovitz number is defined as the ratio of chemical time scale t F {\displaystyle t_{F}} to Kolmogorov time scale t η {\displaystyle t_{\eta }} , named after Béla Karlovitz . [ 1 ] [ 2 ] [ 3 ] The number reads as
In premixed turbulent combustion, the chemical time scale can be defined as t F = D T / S L 2 {\displaystyle t_{F}=D_{T}/S_{L}^{2}} , where D T {\displaystyle D_{T}} is the thermal diffusivity and S L {\displaystyle S_{L}} is the laminar flame speed and the flame thickness is given by δ L = D T / S L {\displaystyle \delta _{L}=D_{T}/S_{L}} , in which case,
where η {\displaystyle \eta } is the Kolmogorov scale. The Karlovitz number is related to Damköhler number as
if the Damköhler number is defined with Kolmogorov scale. If K a < 1 {\displaystyle \mathrm {Ka} <1} , the premixed turbulent flame falls into the category of corrugated flamelets and wrinkled flamelets, otherwise into the thin reaction zone or broken reaction zone flames.
In premixed turbulent combustion, the Klimov–Williams criterion or Klimov–Williams limit , named after A.M. Klimov [ 4 ] [ 5 ] and Forman A. Williams , [ 6 ] is the condition where K a = 1 {\displaystyle \mathrm {Ka} =1} (assuming a Schmidt number of unity). When K a < 1 {\displaystyle \mathrm {Ka} <1} , the flame thickness is smaller than the Kolmogorov scale, thus the flame burning velocity is not affected by the turbulence field. Here, the burning velocity is given by the laminar flame speed and these laminar flamelets are called as wrinkled flamelets or corrugated flamelets, depending on the turbulence intensity. When K a > 1 {\displaystyle \mathrm {Ka} >1} , the turbulent transport penetrates into the preheat zone of the flame (thin reaction zone) or even into the reactive-diffusive zone (distributed flames). | https://en.wikipedia.org/wiki/Karlovitz_number |
The Karlqvist gap or Karlqvist Field is an electromagnetic phenomenon discovered in 1953 by the Swedish engineer Olle Karlqvist (1922-1976), [ 1 ] which is important in magnetic storage for computers. [ 2 ]
Karlqvist discovered the phenomenon while designing a ferromagnetic surface layer to the magnetic drum memory for the BESK computer. [ 1 ] When designing a magnetic memory store, the ferromagnetic layer must be studied to determine the variation of the magnetic field with permeability , air gap, layer thickness and other influencing factors. The problem is non-linear and extremely difficult to solve. Karlqvist's gap discovery shows that the non-linear problem could be approximated by a linear boundary value for the two-dimensional static field and the one-dimensional transient field . This linear calculation gives a first approximation.
Karlqvist published his discovery in the 1954 paper "Calculation of the magnetic field in ferromagnetic layer of a magnetic drum" at KTH Royal Institute of Technology in Stockholm . [ 3 ]
This electromagnetism -related article is a stub . You can help Wikipedia by expanding it .
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karlqvist_gap |
Karlsruhe Accurate Arithmetic ( KAA ), or Karlsruhe Accurate Arithmetic Approach ( KAAA ), augments conventional floating-point arithmetic with good error behaviour with new operations to calculate scalar products with a single rounding error. [ 1 ]
The foundations for KAA were developed at the University of Karlsruhe starting in the late 1960s. [ 2 ] [ 3 ] [ 4 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karlsruhe_Accurate_Arithmetic |
The Karlsruhe Congress was an international meeting of chemists organized by August Kekulé and held in Karlsruhe , Germany from 3 to 5 September 1860. It was the first international conference of chemistry with 140 participants.
The conference is known for the adoption of atomic weights in chemistry motivated by the participation of Stanislao Cannizzaro . During the congress he showed evidence using Avogadro's hypothesis , that certain gases were not made of atoms but of diatomic molecules .
It has been argued [ 1 ] that the Karlsruhe meeting was the first international meeting of chemists and that it led to the eventual founding of the International Union of Pure and Applied Chemistry (IUPAC).
The Karlsruhe Congress was called so that European chemists could discuss matters of chemical nomenclature, notation, and atomic weights. The organization, invitation, and sponsorship of the conference were handled by August Kekulé , Adolphe Wurtz , and Karl Weltzien . [ 2 ] As an example of the problems facing the delegates, Kekulé's Lehrbuch der Organischen Chemie gave nineteen different formulas used by chemists for acetic acid , as shown in the figure on this page. [ 3 ] [ 4 ]
An understanding was reached on the time and place of the meeting, and printing of a circular addressed to European chemists listed below, which explained the objectives and goals of an international congress was agreed upon. The circular concluded: "...with the aim of avoiding any unfortunate omissions, the undersigned request that the individuals to whom this circular will be sent please communicate it to their scientist friends who are duly authorized to attend the planned conference." [ 5 ] The circular of the conference was sent to:
Of the above, only 20 of 45 attended. [ 7 ]
The congress opened in the assembly hall of the Baden Parliament the 3th September, with Weltzien serving as the general secretary. In his address, he highlighted the international and discipline-specific nature of the meeting. Kekulé delivered an opening address. Wurtz documented the proceedings for future publication. A dinner for 120 people was held in the museum hall. [ 8 ] [ 9 ]
The next day, the assembly, led by Weltzien, discussed the committee's proposed theme of the day before regarding the disputed meanings of "atom," "molecule," and "equivalence." However, no conclusions were reached, leading the committee to meet twice on the same day. They decided to present three specific nomenclature proposals to the assembly for further consideration. [ 8 ]
The Karlsruhe meeting started with no firm agreement on the vexing problem of atomic and molecular weights. However, on the meeting's last day reprints of Stanislao Cannizzaro 's 1858 paper on atomic weights, [ 10 ] in which he utilized earlier work by Amedeo Avogadro and André-Marie Ampère , were distributed. Cannizzaro's efforts exerted a heavy and, in some cases, an almost immediate influence on the delegates. Lothar Meyer later wrote that on reading Cannizzaro's paper, [ 11 ] [ 12 ]
I was astonished at its clarity, the little manuscript covered all the important points in dispute. It was as if scales fell from my eyes, doubts vanished, and a feeling of calm certainty came over me.
An important long-term result of the Karlsruhe Congress was the adoption of the now-familiar atomic weights. Prior to the Karlsruhe meeting, and going back to John Dalton's work in 1803, several systems of atomic weights were in use. [ 13 ] In one case, a value of 1 was adopted as the weight of hydrogen (the base unit), with 6 for carbon and 8 for oxygen. As long as there were uncertainties over atomic weights then the compositions of many compounds remained in doubt. Following the Karlsruhe meeting, values of about 1 for hydrogen, 12 for carbon, 16 for oxygen, and so forth were adopted. This was based on a recognition that certain elements, such as hydrogen, nitrogen, and oxygen, were composed of diatomic molecules and not individual atoms.
The number of people who wanted to participate was considerable, and on 3 September 1860, 140 chemists met together in the meeting room of the second Chamber of State, which was made available by the Frederick I, Grand Duke of Baden .
According to Wurtz, the printed list of members, supplemented by handwritten additions, contains 126 names listed below. [ 14 ] | https://en.wikipedia.org/wiki/Karlsruhe_Congress |
In mathematics , the Karoubi conjecture is a conjecture by Max Karoubi ( 1979 ) that the algebraic and topological K-theories coincide on C* algebras spatially tensored with the algebra of compact operators. It was proved by Andrei Suslin and Mariusz Wodzicki ( 1990 , theorem 6, 1992 ).
This abstract algebra -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karoubi_conjecture |
The Karplus equation , named after Martin Karplus , describes the correlation between 3 J-coupling constants and dihedral torsion angles in nuclear magnetic resonance spectroscopy : [ 2 ]
where J is the 3 J coupling constant, ϕ {\displaystyle \phi } is the dihedral angle , and A , B , and C are empirically derived parameters whose values depend on the atoms and substituents involved. [ 3 ] The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2φ rather than cos 2 φ —these lead to different numerical values of A , B , and C but do not change the nature of the relationship.
The relationship is used for 3 J H,H coupling constants. The superscript "3" indicates that a 1 H atom is coupled to another 1 H atom three bonds away, via H-C-C-H bonds. (Such H atoms bonded to neighbouring carbon atoms are termed vicinal ). [ 4 ] The magnitude of these couplings are generally smallest when the torsion angle is close to 90° and largest at angles of 0 and 180°.
This relationship between local geometry and coupling constant is of great value throughout nuclear magnetic resonance spectroscopy and is particularly valuable for determining backbone torsion angles in protein NMR studies. | https://en.wikipedia.org/wiki/Karplus_equation |
The Karrick process is a low-temperature carbonization (LTC) and pyrolysis process of carbonaceous materials. Although primarily meant for coal carbonization , it also could be used for processing of oil shale , lignite or any carbonaceous materials. These are heated at 450 °C (800 °F) to 700 °C (1,300 °F) in the absence of air to distill out synthetic fuels – unconventional oil and syngas . It could be used for a coal liquefaction as also for a semi-coke production. The process was the work of oil shale technologist Lewis Cass Karrick at the United States Bureau of Mines in the 1920s.
The Karrick process was invented by Lewis Cass Karrick in the 1920s. Although Karrick did not invent coal LTC as such, he perfected the existing technologies resulting the Karrick process. [ 1 ] The retort used for the Karrick process based on the Nevada–Texas–Utah Retort , used for the shale oil extraction . [ 2 ]
In 1935, a Karrick LTC pilot plant was constructed in the coal research laboratory at the University of Utah . [ 3 ] Commercial-size processing plants were operated during the 1930s in Colorado , Utah and Ohio . During World War II , similar processing plant was operated by the United States Navy . [ 3 ] In Australia, during World War II the Karrick process plants were used for shale oil extraction in New South Wales. In 1950s–1970s, the technology was used by the Rexco Company in its Snibston plant at Coalville in Leicestershire , England. [ 2 ]
The Karrick process is a low-temperature carbonization process, which uses a hermetic retort. [ 4 ] For commercial scale production, a retort about 3 feet (0.91 m) in diameter and 20 feet (6.1 m) high would be used. The process of carbonization would last about 3 hours. [ 5 ]
Superheated steam is injected continuously into the top of a retort filled by coal. At first, in contact with cool coal, the steam condenses to water acting as a cleaning agent. While temperature of coal rises, the destructive distillation starts. [ 3 ] Coal is heated at 450 °C (800 °F) to 700 °C (1,300 °F) in the absence of air. The carbonization temperature is lower compared with 800 °C (1,500 °F) to 1,000 °C (1,800 °F) for producing metallurgic coke. The lower temperature optimizes the production of coal tars richer in lighter hydrocarbons than normal coal tar, and therefore it is suitable for processing into fuels. [ 4 ] Resulting water, oil and coal tar, and syngas moves out from retort through outlet valves at the bottom of the retort. The residue ( char or semi-coke) remains in the retort. [ 3 ] While the produced liquids are mostly a by-product, the semi-coke is the main product, a solid and smokeless fuel . [ 6 ]
The Karrick LTC process generates no carbon dioxide , but it does produce a significant amount of carbon monoxide .
In the Karrick process, 1 short ton of coal yields up to 1 barrel of oils and coal tars (12% by weight), and produces 3,000 cubic feet (85 m 3 ) of rich coal gas and 1,500 pounds (680 kg) of solid smokeless char or semi-coke (for one metric ton , 0.175 m 3 of oils and coal tars, 95 m 3 of gas, and 750 kg of semi-coke). [ 3 ] [ 4 ] Yields by volume of approximately 25% gasoline , 10% kerosene and 20% good quality fuel oil are obtainable from coal. [ citation needed ] Gasoline obtained from coal by the Karrick process combined with cracking and refining is equal in quality to tetraethyl lead gasolines. [ 3 ] [ 7 ] More power is developed in internal combustion engines and an increase in fuel economy of approximately 20% is obtainable under identical operating conditions. [ 2 ]
Semi-coke can be used for utility boilers and coking coal in steel smelters, yields more heat than raw coal and can be converted to water gas . Water gas can be converted to oil by the Fischer–Tropsch process . [ 4 ] Coal gas from Karrick LTC yields greater energy content than natural gas . Phenolic wastes are used by the chemical industry as feedstock for plastics, etc. Electrical power can be cogenerated at nominal equipment cost. [ 2 ]
Oils, including petroleum, have long been extracted from coal. Production plants were merely shut down in the 1880s because crude oil became cheaper than coal liquefaction. The capability itself, however, has never disappeared. Eight years of pilot plant tests by Karrick attest that states, cities or even smaller towns, could make their own gas and generate their own electricity. [ 3 ]
A 30-ton plant and oil refinery will show a profit over and above all operating and capital costs and the products will sell at attractive prices for equivalent products. The private sector should require no subsidies, but not in competition with those who skim off the oil from coal and sell the residual smokeless fuel to power plants. [ 2 ]
The cheapest liquid fuel from coal will come when processed by LTC for both liquid fuels and electric power. As a tertiary product of the coal distilling process, electrical energy can be generated at a minimum equipment cost. A Karrick LTC plant with 1 kiloton of daily coal capacity produces sufficient steam to generate 100,000 kilowatt hours of electrical power at no extra cost excepting capital investment for electrical equipment and loss of steam temperature passing through turbines. [ 2 ] The process steam cost could be low since this steam could be derived from off-peak boiler capacity or from turbines in central electric stations. Fuel for steam and superheating would subsequently be reduced in cost. [ 2 ]
Compared to the Bergius process , the Karrick process is cheaper, requires less water and destroys less the thermal value (one-half that of the Bergius process). [ 2 ] The smokeless semi-coke fuel, when burned in an open grate or in boilers, delivers 20% to 25% more heat than raw coal. [ 3 ] The coal gas should deliver more heat than natural gas per heat unit contained due to the greater quantity of combined carbon and lower dilution of the combustion gases with water vapor. [ 2 ] | https://en.wikipedia.org/wiki/Karrick_process |
Karsten Meyer (born 17 May 1968 in Herne , Germany ) is a German inorganic chemist and Chair of Inorganic and General Chemistry at the Friedrich-Alexander University of Erlangen-Nürnberg (FAU). [ 1 ] His research involves the coordination chemistry of transition metals as well as uranium coordination chemistry, small molecule activation with these coordination complexes, and the synthesis of new chelating ligands. [ 2 ] [ 3 ] He is the 2017 recipient of the Elhuyar-Goldschmidt Award of the Spanish Royal Society of Chemistry , the Ludwig-Mond Award of the Royal Society of Chemistry , [ 4 ] and the L.A. Chugaev Commemorative Medal of the Russian Academy of Sciences , among other awards. He also serves as an Associate Editor of the journal Organometallics since 2014. [ 5 ] [ 6 ]
Meyer was born on 17 May 1968 in Herne , Germany. [ 7 ] [ 8 ] He studied chemistry at the Ruhr University Bochum , receiving his diploma (in chemistry) in May 1995. [ 8 ] In summer 1995, Meyer then joined the laboratory of Professor Karl Wieghardt at the Max Planck Institute for Radiation Chemistry , where he worked on the synthesis of novel high-valent nitrido complexes of manganese, [ 9 ] chromium [ 10 ] and iron. [ 11 ] These nitrido complexes were generated by the photolysis of the corresponding azido complexes. [ 8 ] Meyer graduated in January 1998 with his Ph.D. He then moved to the Massachusetts Institute of Technology as a DFG Postdoctoral Fellow in 1998 to conduct research in the laboratory of Professor Christopher Cummins . [ 8 ] AT MIT, Meyer worked on amido complexes of uranium with novel amido ligands [ 12 ] and dinitrogen cleavage with heterobimetallic complexes of niobium and molybdenum. [ 13 ]
In 2001, Meyer began his independent career as an assistant professor at the University of California, San Diego . Then in 2006, Meyer moved to the University of Erlangen-Nürnberg as the Chair of the Institute of Inorganic & General Chemistry. [ 14 ]
Meyer's early work featured explored the coordination chemistry of uranium with small molecules such as carbon dioxide [ 15 ] [ 16 ] and light alkanes. [ 17 ] Additionally, Meyer's group synthesized novel tripodal N-heterocyclic carbene ligands [ 18 ] [ 19 ] to stabilize reactive intermediates such as an iron(IV) nitride. [ 20 ] [ 21 ] In 2011, in collaboration with Prof. Jeremy M. Smith's group, Meyer achieved the first synthesis and characterization of a stable iron(V) nitride complex. [ 22 ] [ 23 ] [ 24 ] [ 25 ]
Other research highlights include:
Meyer's hobbies include nature and macro photography , scuba diving, and driving his car on a closed circuit. [ 8 ] | https://en.wikipedia.org/wiki/Karsten_Meyer_(chemist) |
Karyogamy is the final step in the process of fusing together two haploid eukaryotic cells, and refers specifically to the fusion of the two nuclei . Before karyogamy, each haploid cell has one complete copy of the organism's genome . In order for karyogamy to occur, the cell membrane and cytoplasm of each cell must fuse with the other in a process known as plasmogamy . Once within the joined cell membrane, the nuclei are referred to as pronuclei . Once the cell membranes, cytoplasm, and pronuclei fuse, the resulting single cell is diploid , containing two copies of the genome. This diploid cell, called a zygote or zygospore can then enter meiosis (a process of chromosome duplication, recombination, and division, to produce four new haploid cells), or continue to divide by mitosis . Mammalian fertilization uses a comparable process to combine haploid sperm and egg cells ( gametes ) to create a diploid fertilized egg.
The term karyogamy comes from the Greek karyo- (from κάρυον karyon ) 'nut' and γάμος gamos 'marriage'. [ 1 ]
Haploid organisms such as fungi , yeast , and algae can have complex cell cycles , in which the choice between sexual or asexual reproduction is fluid, and often influenced by the environment. Some organisms, in addition to their usual haploid state, can also exist as diploid for a short time, allowing genetic recombination to occur. Karyogamy can occur within either mode of reproduction: during the sexual cycle or in somatic (non-reproductive) cells. [ 2 ]
Thus, karyogamy is the key step in bringing together two sets of different genetic material which can recombine during meiosis. In haploid organisms that lack sexual cycles, karyogamy can also be an important source of genetic variation during the process of forming somatic diploid cells. Formation of somatic diploids circumvents the process of gamete formation during the sexual reproduction cycle and instead creates variation within the somatic cells of an already developed organism, such as a fungus . [ 2 ]
The role of karyogamy in sexual reproduction can be demonstrated most simply by single-celled haploid organisms such as the algae of genus Chlamydomonas or the yeast Saccharomyces cerevisiae . Such organisms exist normally in a haploid state, containing only one set of chromosomes per cell. However, the mechanism remains largely the same among all haploid eukaryotes. [ 3 ]
When subjected to environmental stress, such as nitrogen starvation in the case of Chlamydomonas , cells are induced to form gametes . [ 4 ] Gamete formation in single-celled haploid organisms such as yeast is called sporulation , resulting in many cellular changes that increase resistance to stress. Gamete formation in multicellular fungi occurs in the gametangia , an organ specialized for such a process, usually by meiosis. [ 5 ] When opposite mating types meet, they are induced to leave the vegetative cycle and enter the mating cycle. In yeast, there are two mating types, a and α. [ 6 ] In fungi, there can be two, four, or even up to 10,000 mating types, depending on the species. [ 7 ] [ 8 ] Mate recognition in the simplest eukaryotes is achieved through pheromone signaling, which induces shmoo formation (a projection of the cell) and begins the process of microtubule organization and migration. Pheromones used in mating type recognition are often peptides, but sometimes trisporic acid or other molecules, recognized by cellular receptors on the opposite cell. Notably, pheromone signaling is absent in higher fungi such as mushrooms. [ 3 ]
The cell membranes and cytoplasm of these haploid cells then fuse together in a process known as plasmogamy . This results in a single cell with two nuclei, known as pronuclei . The pronuclei then fuse together in a well regulated process known as karyogamy. This creates a diploid cell known as a zygote , or a zygospore , [ 4 ] which can then enter meiosis , a process of chromosome duplication, recombination, and cell division, to create four new haploid gamete cells. One possible advantage of sexual reproduction is that it results in more genetic variability, providing the opportunity for adaptation through natural selection. Another advantage is efficient recombinational repair of DNA damages during meiosis. Thus, karyogamy is the key step in bringing together a variety of genetic material in order to ensure recombination in meiosis. [ 3 ]
The Amoebozoa is a large group of mostly single-celled species that have recently been determined to have the machinery for karyogamy and meiosis . [ 9 ] Since the Amoeboza branched off early from the eukaryotic family tree, this finding suggests that karyogamy and meiosis were present early in eukaryotic evolution.
The ultimate goal of karyogamy is fusion of the two haploid nuclei. The first step in this process is the movement of the two pronuclei toward each other, which occurs directly after plasmogamy. Each pronucleus has a spindle pole body that is embedded in the nuclear envelope and serves as an attachment point for microtubules . Microtubules, an important fiber-like component of the cytoskeleton , emerge at the spindle pole body. The attachment point to the spindle pole body marks the minus end, and the plus end extends into the cytoplasm . The plus end has normal roles in mitotic division , but during nuclear congression, the plus ends are redirected. The microtubule plus ends attach to the opposite pronucleus, resulting in the pulling of the two pronuclei toward each other. [ 10 ]
Microtubule movement is mediated by a family of motor proteins known as kinesins , such as Kar3 in yeast. Accessory proteins, such as Spc72 in yeast, act as a glue, connecting the motor protein, spindle pole body and microtubule in a structure known as the half-bridge. Other proteins, such as Kar9 and Bim1 in yeast, attach to the plus end of the microtubules. They are activated by pheromone signals to attach to the shmoo tip. A shmoo is a projection of the cellular membrane which is the site of initial cell fusion in plasmogamy. After plasmogamy, the microtubule plus ends continue to grow towards the opposite pronucleus. It is thought that the growing plus end of the microtubule attaches directly to the motor protein of the opposite pronucleus, triggering a reorganization of the proteins at the half-bridge. The force necessary for migration occurs directly in response to this interaction. [ 11 ]
Two models of nuclear congression have been proposed: the sliding cross-bridge, and the plus end model. In the sliding cross-bridge model, the microtubules run antiparallel to each other for the entire distance between the two pronuclei, forming cross-links to each other, and each attaching to the opposite nucleus at the plus end. This is the favored model. The alternative model proposes that the plus ends contact each other midway between the two pronuclei and only overlap slightly. In either model, it is believed that microtubule shortening occurs at the plus end and requires Kar3p (in yeast), a member of a family of kinesin -like proteins. [ 10 ]
Microtubule organization in the cytoskeleton has been shown to be essential for proper nuclear congression during karyogamy. Defective microtubule organization causes total failure of karyogamy, but does not totally interrupt meiosis and spore production in yeast. The failure occurs because the process of nuclear congression cannot occur without functional microtubules. Thus, the pronuclei do not approach close enough to each other to fuse together, and their genetic material remains separated. [ 12 ]
Merging of the nuclear envelopes of the pi occurs in three steps: fusion of the outer membrane, fusion of the inner membrane, and fusion of the spindle pole bodies. In yeast, several members of the Kar family of proteins, as well as a protamine , are required for the fusion of nuclear membranes. The protamine Prm3 is located on the outer surface of each nuclear membrane, and is required for the fusion of the outer membrane. The exact mechanism is not known. Kar5, a kinesin-like protein, is necessary to expand the distance between the outer and inner membranes in a phenomenon known as bridge expansion. Kar8 and Kar2 are thought to be necessary to the fusing of the inner membranes. [ 13 ] As described above, the reorganization of accessory and motor proteins during pronuclear migration also serves to orient the spindle pole bodies in the correct direction for efficient nuclear congression. Nuclear congression can still take place without this pre-orientation of spindle pole bodies, but it is slower. Ultimately the two pronuclei combine the contents of their nucleoplasms and form a single envelope around the result. [ 11 ]
Although fungi are normally haploid, diploid cells can arise by two mechanisms. The first is a failure of the mitotic spindle during regular cell division, and does not involve karyogamy. The resulting cell can only be genetically homozygous since it is produced from one haploid cell. The second mechanism, involving karyogamy of somatic cells, can produce heterozygous diploids if the two nuclei differ in genetic information. The formation of somatic diploids is generally rare, and is thought to occur because of a mutation in the karyogamy repressor gene (KR). [ 2 ]
There are, however, a few fungi that exist mostly in the diploid state. One example is Candida albicans , a fungus that lives in the gastrointestinal tracts of many warm blooded animals, including humans. Although usually innocuous, C. albicans can turn pathogenic and is a particular problem in immunosuppressed patients. Unlike with most other fungi, diploid cells of different mating types fuse to create tetraploid cells which subsequently return to the diploid state by losing chromosomes. [ 14 ]
Mammals, including humans, also combine genetic material from two sources - father and mother - in fertilization . This process is similar to karyogamy. As with karyogamy, microtubules play an important part in fertilization and are necessary for the joining of the sperm and egg ( oocyte ) DNA. [ 15 ] Drugs such as griseofulvin that interfere with microtubules prevent the fusion of the sperm and egg pronuclei. The gene KAR2 which plays a large role in karyogamy has a mammalian analog called Bib/GRP78. [ 16 ] In both cases, genetic material is combined to create a diploid cell that has greater genetic diversity than either original source. [ 17 ] Instead of fusing in the same way as lower eukaryotes do in karyogamy, the sperm nucleus vesiculates and its DNA decondenses. The sperm centriole acts as a microtubule organizing center and forms an aster which extends throughout the egg until contacting the egg's nucleus. The two pronuclei migrate toward each other and then fuse to form a diploid cell. [ 18 ] | https://en.wikipedia.org/wiki/Karyogamy |
Karyoklepty ( / ˌ k æ r i ˈ oʊ k l ɛ p t i / KARR -ee- OH -klep-tee ) is a strategy for cellular evolution , whereby a predator cell appropriates the nucleus of a cell from another organism to supplement its own biochemical capabilities. [ 1 ]
In the related process of kleptoplasty , the predator sequesters plastids (especially chloroplasts ) from dietary algae . The chloroplasts can still photosynthesize , but do not last long after the prey's cells are metabolised. If the predator can also sequester cell nuclei from the prey to encode proteins for the plastids, it can sustain them. Karyoklepty is this sequestration of nuclei; even after sequestration, the nuclei are still capable of transcription .
Johnson et al. described and named karyoklepty in 2007 after observing it in the ciliate species Mesodinium rubrum . [ 1 ] Karyoklepty is a Greek compound of the words karydi ("kernel") and kleftis ("thief"). [ 1 ] | https://en.wikipedia.org/wiki/Karyoklepty |
Karyolysis (from Greek κάρυον karyon— kernel, seed, or nucleus ), and λύσις lysis from λύειν lyein , "to separate") is the complete dissolution of the chromatin of a dying cell due to the enzymatic degradation by endonucleases . The whole cell will eventually stain uniformly with eosin after karyolysis. It is usually associated with karyorrhexis and occurs mainly as a result of necrosis , while in apoptosis after karyorrhexis the nucleus usually dissolves into apoptotic bodies . [ 1 ]
Disintegration of the cytoplasm , pyknosis of the nuclei, and karyolysis of the nuclei of scattered transitional cells may be seen in urine from healthy individuals as well as in urine containing malignant cells. Cells with an attached tag of partially preserved cytoplasm were initially described by Papanicolaou and are sometimes called comet or decoy cells. They may have some of the characteristics of malignancy, and it is therefore important that they be recognized for what they are. [ 2 ]
Karyolysis is the culminating step in the process of necrosis. Necrosis is a form of cellular injury in which living tissue experiences irreversible damage through premature cell death. While both are forms of cell death, necrosis differs from apoptosis as an external factor triggers necrosis rather than it being a controlled and planned process.
First, it is essential to understand the factors that can trigger a necrotic reaction. A typical example is ischemia , also known as reduced blood flow, in which the interrupted or decreased blood supply cannot sufficiently supply oxygen and nutrients, leading to necrosis. In this situation, blood flow restriction will deprive cells of oxygen (hypoxia), impairing cellular respiration and energy production. Ischemia triggers ATP depletion and accumulation of metabolic waste, leading to cell death. This process can occur in myocardial infarctions (heart attacks), where a blood clot blocks coronary arteries , and the lack of blood flow through said arteries causes heart muscle cell necrosis.
Some more commonly seen triggers of necrosis include physical trauma (such as crush injuries, burns, and frostbite ), viral/bacterial infections, chemical/toxicant exposure, immune reactions (autoimmune and inflammatory), radiation exposure, and oxidative stress . While there are many causes of necrosis, the basic principle remains: an external factor affects the cells or tissue unexpectedly, eliciting a reaction of steps that terminates the cells prematurely.
Necrosis involves the nucleus undergoing an integral series of morphological changes that are critical indicators of the cell's deterioration. The three steps are pyknosis, karyorrhexis, and terminating in karyolysis.
Pyknosis (stemming from the Greek pyknos (πυκνός), meaning "dense" or "thick") is the first step in which the nucleus condenses, reflecting the root meaning. During pyknosis, the chromatin within the nucleus clumps together, resulting in a shrunken, hyperchromatic nucleus, seen as a compact and dark form in microscopic views; this dense appearance is characteristic of the cell preparing for the following stages of necrosis. Pyknosis is unique to the other steps of necrosis in that it is the only step that commonly occurs the same way in processes other than necrosis. While karyorrhexis and karyolysis are typically associated with necrosis (or in the case of karyorrhexis, has different mechanisms in apoptosis and necrosis), pyknosis is a characteristic step observed in both necrosis and apoptosis, as well as some normal cell differentiation–an example of this being normal erythrocyte (red blood cell) maturation.
Following pyknosis, karyorrhexis (stemming from the Greek karyo- (κάρυον), meaning "nut" or "nucleus," with rhexis (ῥῆξις), meaning "bursting" or "breaking") ensues in which the nucleus fragments or bursts. During this phase, the nuclear envelope breaks down, causing the condensed chromatin to break apart and then distribute nuclear fragments throughout the cytoplasm. Karyorrhexis occurs in apoptosis– with a different cause and purpose than necrosis–and, on rare occasions, occurs in normal cell differentiation processes. The difference between apoptotic and necrotic karyorrhexis is essential to the karyolytic process and incidence. In an apoptotic cell, following chromatin condensation (pyknosis), the nucleus fragments in an organized way, breaking down into small, membrane-bound apoptotic bodies. Each body contains a portion of the nucleus and cytoplasmic material, neatly packaged. These fragmented and packaged membrane-bound bodies then signal nearby phagocytic cells (such as macrophages ) to engulf them. This entire process serves as a clean removal process. It prevents the release of cellular contents into surrounding tissue and extracellular space , thus minimizing damage to neighboring cells and avoiding an inflammatory response. This measure is essential for maintaining normal tissue health when cells die, which is imperative to a cell's typical life cycle.
Karyorrhexis also follows pyknosis along the necrotic pathway; however, in the case of necrosis, the inducing stimulus causes the nuclear envelope and chromatin to break down chaotically. This disorganization of broken nuclear content and chromatin is the immediate difference between apoptosis and necrosis pathways, apart from the signal causing them, in which the steps will differ hereafter. The unregulated fragmentation causes the dispersal of nuclear fragments throughout the cytoplasm without an intentional or organized method to dispose of them from there. Biological reasons for the nuclear envelope and chromatin break down differently could be any of the following factors:
The last of these factors is significant in that it furthers the effects of a necrotic cell by eliciting necrosis in neighboring cells (localized response of cell death) as they recognize leaked cellular contents in the extracellular space as signs of damage.
The third and final step in the necrotic pathway is karyolysis (stemming from roots karyo- (κάρυον), meaning "nut" or "nucleus," and lysis (λύσις), meaning "dissolution" or "loosening"). The remaining nuclear fragments from karyorrhexis degrade completely during this step. Necrosis, including karyolysis, concludes with complete disintegration of the cell. After karyolysis, the cell undergoes total degradation, often called "cytoplasmic dissolution" or " ghost cell formation," leaving behind cytoplasmic debris and inflammatory mediators in the extracellular space. Here is how the process ties together:
Additionally, karyolysis occurs in necrosis and necroptosis but with key differences. In necrosis, karyolysis results from chaotic enzymatic degradation of nuclear material following lysosomal membrane permeabilization (LMP), driven by external stressors such as trauma or ischemia. In contrast, necroptosis, a regulated form of cell death different from both necrosis and apoptosis and serving almost as a blend, involves the same terminal event of karyolysis but within a programmed framework. [ 5 ] The RIPK1-RIPK3-MLKL signaling axis directs the process, ensuring controlled steps before membrane rupture. [ 6 ] Although both necrosis and necroptosis release intracellular contents that trigger inflammation, the regulated nature of necroptosis offers potential for targeted therapeutic intervention, especially in diseases where excessive or uncontrolled karyolysis contributes to pathology. [ 6 ]
The enzymes involved in this process are critical in understanding karyolysis.
Key enzymes involved in karyolysis include deoxyribonucleases (DNases), ribonucleases (RNases), proteases , and lysozymes . [ 7 ]
Mechanisms of these enzymatic reactions often link to lysosomal membrane permeabilization (LMP). [ 7 ] LMP occurs under stressed conditions, releasing hydrolytic enzymes from the internal portion of the lysosome into the cytosol. [ 5 ] [ 3 ] Various factors, such as oxidative stress, exposure to lysosomotropic agents, or the action of specific lipids, can spur LMP. [ 4 ] Once hydrolytic enzymes–DNases, RNases, and proteases–are freed from lysosomes, they translocate to the nucleus. [ 3 ] Without lysosomal sequestration, the active enzymes can unintentionally and chaotically degrade nuclear components. In conjunction with other karyolytic mechanisms, the concerted action of these enzymes causes the nucleus to lose structural integrity and staining properties, a hallmark of karyolysis in microscopy.
Specifically, it is DNA cleavage, in which DNases cut chromatin into smaller fragments until eventually reducing it to mononucleotides or oligonucleotides , contributing to the "ghost" nucleus appearance since degraded DNA is no longer detectable with basic dyes. Another case is proteases, which target histones for degradation; histones function to bind and protect DNA, so degradation augments DNases enzymatic attack due to the lack of histone protection. Additionally, proteins like nuclear lamins–typically providing structural support to the nuclear envelope–are degrading, contributing to the disintegration of the nuclear structure. Finally, RNases target ribosomal ( rRNA ) and messenger RNA ( mRNA ) within the nucleus in RNA degradation, completing the dissolution of nuclear contents. While the mechanisms above reflect the general sequence of events making up karyolysis, these enzymatic reactions are dynamic and interdependent, with many processes occurring concurrently. The release of lysosomal enzymes occurs first and triggers multiple enzymatic reactions due to the chaotic release of typically contained enzymes. DNases and RNases act on DNA and RNA contemporaneously, while proteases also work to degrade histones and other structural proteins. | https://en.wikipedia.org/wiki/Karyolysis |
The karyorelictid nuclear code (translation table 27) is a genetic code used by the nuclear genome of the Karyorelictea ciliate Parduczia sp. [ 1 ] This code, along with translation tables 28 and 31, is remarkable in that every one of the 64 possible codons can be a sense codon. Translation termination probably relies on context, specifically proximity to the poly(A) tail. [ 2 ]
Bases: adenine (A), cytosine (C), guanine (G) and thymine (T) or uracil (U).
Amino acids: Alanine (Ala, A), Arginine (Arg, R), Asparagine (Asn, N), Aspartic acid (Asp, D), Cysteine (Cys, C), Glutamic acid (Glu, E), Glutamine (Gln, Q), Glycine (Gly, G), Histidine (His, H), Isoleucine (Ile, I), Leucine (Leu, L), Lysine (Lys, K), Methionine (Met, M), Phenylalanine (Phe, F), Proline (Pro, P), Serine (Ser, S), Threonine (Thr, T), Tryptophan (Trp, W), Tyrosine (Tyr, Y), and Valine (Val, V).
This article incorporates text from the United States National Library of Medicine , which is in the public domain . [ 1 ] | https://en.wikipedia.org/wiki/Karyorelict_nuclear_code |
Karyorrhexis (from Greek κάρυον karyon 'kernel, seed, nucleus' and ῥῆξις rhexis 'bursting') is the destructive fragmentation of the nucleus of a dying cell [ 1 ] whereby its chromatin is distributed irregularly throughout the cytoplasm. [ 2 ] It is usually preceded by pyknosis and can occur as a result of either programmed cell death (apoptosis), cellular senescence , or necrosis . [ citation needed ]
In apoptosis , the cleavage of DNA is done by Ca 2+ and Mg 2+ -dependent endonucleases . [ citation needed ]
During apoptosis , a cell goes through a series of steps as it eventually breaks down into apoptotic bodies, which undergo phagocytosis . In the context of karyorrhexis, these steps are, in chronological order, pyknosis (the irreversible condensation of chromatin), karyorrhexis (fragmentation of the nucleus and condensed DNA) and karyolysis (dissolution of the chromatin due to endonucleases).
Karyorrhexis involves the breakdown of the nuclear envelope and the fragmentation of condensed chromatin due to endonucleases. In cases of apoptosis, karyorrhexis ensures that nuclear fragments are quickly removed by phagocytes. In necrosis, however, this step fails to progress in an orderly manner, leaving behind fragmented cellular debris, further contributing to tissue damage and inflammation. [ 3 ]
In the intrinsic pathway of apoptosis, environmental factors such as oxidative stress signal pro-apoptotic members of the Bcl-2 protein family to eventually break the outer membrane of the mitochondria. [ 4 ] This causes cytochrome c to leak into the cytoplasm, which causes a cascade of events that eventually leads to the activation of several caspases . [ 4 ] One of these caspases, caspase-6 , is known to cleave nuclear lamina proteins such as lamin A/C , which hold the nuclear envelope together, thereby aiding in the dissolution of the nuclear envelope. [ 5 ]
In the process of karyorrhexis through apoptosis, DNA is fragmented in an orderly manner by endonucleases such as caspase-activated DNase and discrete nucleosomal units are formed. [ 6 ] This is because the DNA has already been condensed during pyknosis, meaning it has been wrapped around histones in an organized manner, with around 180 base pairs per histone. The fragmented chromatin observed during karyorrhexis is made when activated endonucleases cleave the DNA in between the histones, resulting in orderly, discrete nucleosomal units. [ 7 ] These short DNA fragments left by the endonucleases can be identified on an agar gel during electrophoresis due to their unique “laddered” appearance, allowing researchers to better identify cell death through apoptosis. [ 8 ]
Karyorrhexis is associated with a controlled breakdown of the nuclear envelope, typically by caspases that destroy lamins during apoptosis. However, for other forms of cell death that are less controlled than apoptosis, such as necrosis (unprogrammed cell death), the degradation of the nucleus is caused by other factors. Unlike apoptosis, necrosis cells are characterized by having a ruptured plasma membrane, no association with the activation of caspases, and typically invoking an inflammatory response. [ 3 ] Because necrosis is a caspase-independent process, the nucleus may stay intact during early stages of cell death before being ripped open due to osmotic stress and other factors associated with having a hole in the plasma membrane. A specialized form of necrosis, called necroptosis , has a slightly more controlled degradation of the nucleus. This process is dependent on calpain , which is a protease that also degrades lamins, destabilizing the structure of the nucleus. [ 3 ] However, similar to necrosis, this process also involves a ruptured plasma membrane, which contributes to the uncontrolled degradation of the nuclear envelope.
Unlike karyorrhexis in apoptosis which produces apoptotic bodies to be digested through phagocytosis, karyorrhexis in necroptosis leads to the expulsion of cell contents into extracellular space to be digested through pinocytosis . [ 9 ]
The process of apoptosis, and thereby nucleus degradation through karyorrhexis, is invoked by various physiological and pathological stimuli. DNA damage, oxidative stress, hypoxia , and infections can initiate signaling cascades leading to nuclear degradation through the intrinsic pathway of apoptosis. The intrinsic pathway can also be induced through ethanol , which activates apoptosis-related proteins such as BAX and caspases. [ 10 ] Additionally, if the death receptors on a cell’s surface are activated, such as CD95 , the activation of caspases and nuclear envelope degradation can be triggered as well. [ 5 ] In all of these processes, caspases such as caspase-3 play a key role by cleaving nuclear lamins and promoting chromatin fragmentation. [ 3 ] In necrosis, uncontrolled calcium influx and activation of proteases such as calpains accelerate the process, highlighting the contrasting regulatory mechanisms between necrotic and apoptotic karyorrhexis. [ 11 ]
The level of DNA damage determines whether a cell undergoes apoptosis or cell senescence . Cellular senescence refers to the cessation of the cell cycle and thus cell division, which can be observed after a fixed amount (approximately 50) of doublings in primary cells. [ 12 ] One cause of cellular senescence is DNA damage through the shortening of telomeres . This causes a DNA damage response (DDR), which, if prolonged over a long period of time, activates ATR and ATM damage kinases. These kinases activate two more kinases, Chk1 and Chk2 kinases, which can alter the cell in a few different ways. One of these ways is by activating a transcription factor known as p53 . If the level of DNA damage is mild, the p53 will opt to activate CIP , which inhibits CDKs , arresting the cell cycle. However, if the level of DNA damage is severe enough, p53 can trigger apoptotic pathways which lead to the dissolution of the nuclear envelope through karyorrhexis. [ 13 ]
Karyorrhexis is a prominent feature in conditions related to cell death, such as ischemia and neurodegenerative disorders . It has been observed during myocardial infarction and brain stroke , indicating its contribution to cell death in acute stress responses. [ 14 ] Moreover, disorders such as placental vascular malperfusion have highlighted the role of karyorrhexis in fetal demise, particularly when it disrupts normal tissue homeostasis. [ 15 ]
In cancer, apoptotic karyorrhexis plays a dual role. While it facilitates controlled cell death, aiding in tumor suppression, resistance to apoptosis in cancer cells results in evasion of this pathway, promoting malignancy. Therapeutic interventions targeting apoptotic pathways attempt to restore this phase of nuclear degradation to induce tumor regression. [ 16 ]
This cell biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Karyorrhexis |
A karyosome or karyosphere is a dense bundle of chromatin inside the nucleus of a cell within an organism. These bundles are joined together in a limited nuclear volume, but this only happens when the cell is not undergoing meiotic division . Research suggests that within its bundles there is an absence of RNA synthesis occurring in the karyosphere. [ 1 ] This suggests that RNA is actively being carried out within meiosis, especially throughout the first and second prophase of meiotic division.
Karyosomes are formed in several animal classes and have a role in oogenesis , a vital process in female gamete development. The gametes can only develop if the mother has oocytes, [ 1 ] that are rich in cytoplasm, maternal proteins and contain karyosomes.
Karyosomes are known to be very organized. Any mutation that alters the formation and alignment of karyosomes can lead to defects of an oocyte. Defects can also occur with the absence of nucleosomal histone kinase-1. NHK-1 is a kinase that is essential for all karyosomes, for their maintenance and overall formation. NHK-1 is conserved from nematodes to humans. In the absence of NHK-1, karyosome patterns will fall apart within the female's oocyte, and this disruption will lead to problems previously mentioned. [ 2 ] There are other causes of mutations, however they are not fully understood.
The formation of karyosomes is still unclear, but NHK-1 substrates may help understand how the karyosome forms during female meiosis. [ 2 ]
Even though the molecular pathway for this process is to be confirmed, it is known that karyosomes tend to formulate at different stages for different organisms. In insects this occurs in the diplotene stage, a prolonged segment that crosses over genes between homologous chromosomes, and aids in the creation of gametes. For example, this occurs within Drosophila oocytes. The formation of karyosomes during this period are based on a ratio. This ratio is dependent on the potential size of an organism, meaning that typically larger organisms will have bigger karyosomes. [ citation needed ] In other words, a typical Drosophila oocyte is 20 μm in diameter with karyosomes each expected to be about 1 μm in diameter. [ citation needed ]
Structures called karyosomes are present in the nuclei of certain Entamoeba species. [ 3 ]
As oogenesis continues, the karyosome is typically covered by a sheath, known as a capsule. These capsules are created from the interaction between nuclear structures, the nuclear membrane and chromosomes. Karyosomes can also form without a capsule, such as in Drosophila . The function and molecular composition of karyosome capsules are quite unknown. It has been suggested that these [ 4 ] capsules may be a storage site for nuclear ribonucleoprotein particles . Therefore, the absence of this capsule within certain organisms may demonstrate a reduction in small nuclear proteins and RNA. | https://en.wikipedia.org/wiki/Karyosome |
A karyotype is the general appearance of the complete set of chromosomes in the cells of a species or in an individual organism, mainly including their sizes, numbers, and shapes. [ 1 ] [ 2 ] Karyotyping is the process by which a karyotype is discerned by determining the chromosome complement of an individual, including the number of chromosomes and any abnormalities.
A karyogram or idiogram is a graphical depiction of a karyotype, wherein chromosomes are generally organized in pairs, ordered by size and position of centromere for chromosomes of the same size. Karyotyping generally combines light microscopy and photography in the metaphase of the cell cycle , and results in a photomicrographic (or simply micrographic) karyogram. In contrast, a schematic karyogram is a designed graphic representation of a karyotype. In schematic karyograms, just one of the sister chromatids of each chromosome is generally shown for brevity, and in reality they are generally so close together that they look as one on photomicrographs as well unless the resolution is high enough to distinguish them. The study of whole sets of chromosomes is sometimes known as karyology .
Karyotypes describe the chromosome count of an organism and what these chromosomes look like under a light microscope . Attention is paid to their length, the position of the centromeres , banding pattern, any differences between the sex chromosomes , and any other physical characteristics. [ 3 ] The preparation and study of karyotypes is part of cytogenetics .
The basic number of chromosomes in the somatic cells of an individual or a species is called the somatic number and is designated 2n . In the germ-line (the sex cells) the chromosome number is n (humans: n = 23). [ 4 ] [ 5 ] p28 Thus, in humans 2n = 46.
So, in normal diploid organisms, autosomal chromosomes are present in two copies. There may, or may not, be sex chromosomes . Polyploid cells have multiple copies of chromosomes and haploid cells have single copies.
Karyotypes can be used for many purposes; such as to study chromosomal aberrations , cellular function, taxonomic relationships, medicine and to gather information about past evolutionary events ( karyosystematics ). [ 6 ]
The study of karyotypes is made possible by staining . Usually, a suitable dye , such as Giemsa , [ 8 ] is applied after cells have been arrested during cell division by a solution of colchicine usually in metaphase or prometaphase when most condensed. In order for the Giemsa stain to adhere correctly, all chromosomal proteins must be digested and removed. For humans, white blood cells are used most frequently because they are easily induced to divide and grow in tissue culture . [ 9 ] Sometimes observations may be made on non-dividing ( interphase ) cells. The sex of an unborn fetus can be predicted by observation of interphase cells (see amniotic centesis and Barr body ).
Six different characteristics of karyotypes are usually observed and compared: [ 10 ]
A full account of a karyotype may therefore include the number, type, shape and banding of the chromosomes, as well as other cytogenetic information.
Variation is often found:
Both the micrographic and schematic karyograms shown in this section have a standard chromosome layout, and display darker and lighter regions as seen on G banding , which is the appearance of the chromosomes after treatment with trypsin (to partially digest the chromosomes) and staining with Giemsa stain . Compared to darker regions, the lighter regions are generally more transcriptionally active, with a greater ratio of coding DNA versus non-coding DNA , and a higher GC content . [ 11 ]
Both the micrographic and schematic karyograms show the normal human diploid karyotype, which is the typical composition of the genome within a normal cell of the human body, and which contains 22 pairs of autosomal chromosomes and one pair of sex chromosomes (allosomes). A major exception to diploidy in humans is gametes (sperm and egg cells) which are haploid with 23 unpaired chromosomes, and this ploidy is not shown in these karyograms. The micrographic karyogram is converted into grayscale , whereas the schematic karyogram shows the purple hue as typically seen on Giemsa stain (and is a result of its azure B component, which stains DNA purple). [ 14 ]
The schematic karyogram in this section is a graphical representation of the idealized karyotype. For each chromosome pair, the scale to the left shows the length in terms of million base pairs , and the scale to the right shows the designations of the bands and sub-bands . Such bands and sub-bands are used by the International System for Human Cytogenomic Nomenclature to describe locations of chromosome abnormalities . Each row of chromosomes is vertically aligned at centromere level.
Based on the karyogram characteristics of size, position of the centromere and sometimes the presence of a chromosomal satellite (a segment distal to a secondary constriction ), the human chromosomes are classified into the following groups: [ 15 ]
Alternatively, the human genome can be classified as follows, based on pairing, sex differences, as well as location within the cell nucleus versus inside mitochondria :
Schematic karyograms generally display a DNA copy number corresponding to the G 0 phase of the cellular state (outside of the replicative cell cycle ) which is the most common state of cells. The schematic karyogram in this section also shows this state. In this state (as well as during the G 1 phase of the cell cycle ), each cell has two autosomal chromosomes of each kind (designated 2n), where each chromosome has one copy of each locus , making a total copy number of two for each locus (2c). At top center in the schematic karyogram, it also shows the chromosome 3 pair after having undergone DNA synthesis , occurring in the S phase (annotated as S) of the cell cycle. This interval includes the G 2 phase and metaphase (annotated as "Meta."). During this interval, there is still 2n, but each chromosome will have two copies of each locus, wherein each sister chromatid (chromosome arm) is connected at the centromere, for a total of 4c. [ 17 ] The chromosomes on micrographic karyograms are in this state as well, because they are generally micrographed in metaphase, but during this phase the two copies of each chromosome are so close to each other that they appear as one unless the image resolution is high enough to distinguish them. In reality, during the G 0 and G 1 phases, nuclear DNA is dispersed as chromatin and does not show visually distinguishable chromosomes even on micrography.
The copy number of the human mitochondrial genome per human cell varies from 0 (erythrocytes) [ 18 ] up to 1,500,000 ( oocytes ), mainly depending on the number of mitochondria per cell. [ 19 ]
Although the replication and transcription of DNA is highly standardized in eukaryotes , the same cannot be said for their karyotypes, which are highly variable. There is variation between species in chromosome number, and in detailed organization, despite their construction from the same macromolecules . This variation provides the basis for a range of studies in evolutionary cytology .
In some cases there is even significant variation within species. In a review, Godfrey and Masters conclude:
In our view, it is unlikely that one process or the other can independently account for the wide range of karyotype structures that are observed ... But, used in conjunction with other phylogenetic data, karyotypic fissioning may help to explain dramatic differences in diploid numbers between closely related species, which were previously inexplicable. [ 20 ]
Although much is known about karyotypes at the descriptive level, and it is clear that changes in karyotype organization has had effects on the evolutionary course of many species, it is quite unclear what the general significance might be.
We have a very poor understanding of the causes of karyotype evolution, despite many careful investigations ... the general significance of karyotype evolution is obscure.
Instead of the usual gene repression, some organisms go in for large-scale elimination of heterochromatin , or other kinds of visible adjustment to the karyotype.
A spectacular example of variability between closely related species is the muntjac , which was investigated by Kurt Benirschke and Doris Wurster . The diploid number of the Chinese muntjac, Muntiacus reevesi , was found to be 46, all telocentric . When they looked at the karyotype of the closely related Indian muntjac, Muntiacus muntjak , they were astonished to find it had female = 6, male = 7 chromosomes. [ 28 ]
They simply could not believe what they saw ... They kept quiet for two or three years because they thought something was wrong with their tissue culture ... But when they obtained a couple more specimens they confirmed [their findings].
The number of chromosomes in the karyotype between (relatively) unrelated species is hugely variable. The low record is held by the nematode Parascaris univalens , where the haploid n = 1; and an ant: Myrmecia pilosula . [ 30 ] The high record would be somewhere amongst the ferns , with the adder's tongue fern Ophioglossum ahead with an average of 1262 chromosomes. [ 31 ] Top score for animals might be the shortnose sturgeon Acipenser brevirostrum at 372 chromosomes. [ 32 ] The existence of supernumerary or B chromosomes means that chromosome number can vary even within one interbreeding population; and aneuploids are another example, though in this case they would not be regarded as normal members of the population.
The fundamental number, FN , of a karyotype is the number of visible major chromosomal arms per set of chromosomes. [ 33 ] [ 34 ] Thus, FN ≤ 2 × 2n, the difference depending on the number of chromosomes considered single-armed ( acrocentric or telocentric ) present. Humans have FN = 82, [ 35 ] due to the presence of five acrocentric chromosome pairs: 13 , 14 , 15 , 21 , and 22 (the human Y chromosome is also acrocentric). The fundamental autosomal number or autosomal fundamental number, FNa [ 36 ] or AN , [ 37 ] of a karyotype is the number of visible major chromosomal arms per set of autosomes (non- sex-linked chromosomes ).
Ploidy is the number of complete sets of chromosomes in a cell.
Polyploid series in related species which consist entirely of multiples of a single basic number are known as euploid .
In many instances, endopolyploid nuclei contain tens of thousands of chromosomes (which cannot be exactly counted). The cells do not always contain exact multiples (powers of two), which is why the simple definition 'an increase in the number of chromosome sets caused by replication without cell division' is not quite accurate.
This process (especially studied in insects and some higher plants such as maize) may be a developmental strategy for increasing the productivity of tissues which are highly active in biosynthesis. [ 46 ]
The phenomenon occurs sporadically throughout the eukaryote kingdom from protozoa to humans; it is diverse and complex, and serves differentiation and morphogenesis in many ways. [ 47 ]
Aneuploidy is the condition in which the chromosome number in the cells is not the typical number for the species. This would give rise to a chromosome abnormality such as an extra chromosome or one or more chromosomes lost. Abnormalities in chromosome number usually cause a defect in development. Down syndrome and Turner syndrome are examples of this.
Aneuploidy may also occur within a group of closely related species. Classic examples in plants are the genus Crepis , where the gametic (= haploid) numbers form the series x = 3, 4, 5, 6, and 7; and Crocus , where every number from x = 3 to x = 15 is represented by at least one species. Evidence of various kinds shows that trends of evolution have gone in different directions in different groups. [ 48 ] In primates, the great apes have 24x2 chromosomes whereas humans have 23x2. Human chromosome 2 was formed by a merger of ancestral chromosomes, reducing the number. [ 49 ]
Some species are polymorphic for different chromosome structural forms. [ 50 ] The structural variation may be associated with different numbers of chromosomes in different individuals, which occurs in the ladybird beetle Chilocorus stigma , some mantids of the genus Ameles , [ 51 ] the European shrew Sorex araneus . [ 52 ] There is some evidence from the case of the mollusc Thais lapillus (the dog whelk ) on the Brittany coast, that the two chromosome morphs are adapted to different habitats. [ 53 ]
The detailed study of chromosome banding in insects with polytene chromosomes can reveal relationships between closely related species: the classic example is the study of chromosome banding in Hawaiian drosophilids by Hampton L. Carson .
In about 6,500 sq mi (17,000 km 2 ), the Hawaiian Islands have the most diverse collection of drosophilid flies in the world, living from rainforests to subalpine meadows . These roughly 800 Hawaiian drosophilid species are usually assigned to two genera, Drosophila and Scaptomyza , in the family Drosophilidae .
The polytene banding of the 'picture wing' group, the best-studied group of Hawaiian drosophilids, enabled Carson to work out the evolutionary tree long before genome analysis was practicable. In a sense, gene arrangements are visible in the banding patterns of each chromosome. Chromosome rearrangements, especially inversions , make it possible to see which species are closely related.
The results are clear. The inversions, when plotted in tree form (and independent of all other information), show a clear "flow" of species from older to newer islands. There are also cases of colonization back to older islands, and skipping of islands, but these are much less frequent. Using K-Ar dating, the present islands date from 0.4 million years ago (mya) ( Mauna Kea ) to 10mya ( Necker ). The oldest member of the Hawaiian archipelago still above the sea is Kure Atoll , which can be dated to 30 mya. The archipelago itself (produced by the Pacific Plate moving over a hot spot ) has existed for far longer, at least into the Cretaceous . Previous islands now beneath the sea ( guyots ) form the Emperor Seamount Chain . [ 54 ]
All of the native Drosophila and Scaptomyza species in Hawaiʻi have apparently descended from a single ancestral species that colonized the islands, probably 20 million years ago. The subsequent adaptive radiation was spurred by a lack of competition and a wide variety of niches . Although it would be possible for a single gravid female to colonise an island, it is more likely to have been a group from the same species. [ 55 ] [ 56 ] [ 57 ] [ 58 ]
There are other animals and plants on the Hawaiian archipelago which have undergone similar, if less spectacular, adaptive radiations. [ 59 ] [ 60 ]
Chromosomes display a banded pattern when treated with some stains. Bands are alternating light and dark stripes that appear along the lengths of chromosomes. Unique banding patterns are used to identify chromosomes and to diagnose chromosomal aberrations, including chromosome breakage, loss, duplication, translocation or inverted segments. A range of different chromosome treatments produce a range of banding patterns: G-bands, R-bands, C-bands, Q-bands, T-bands and NOR-bands.
Cytogenetics employs several techniques to visualize different aspects of chromosomes: [ 9 ]
In the "classic" (depicted) karyotype, a dye , often Giemsa (G-banding) , less frequently mepacrine (quinacrine) , is used to stain bands on the chromosomes. Giemsa is specific for the phosphate groups of DNA . Quinacrine binds to the adenine - thymine -rich regions. Each chromosome has a characteristic banding pattern that helps to identify them; both chromosomes in a pair will have the same banding pattern.
Karyotypes are arranged with the short arm of the chromosome on top, and the long arm on the bottom. Some karyotypes call the short and long arms p and q , respectively. In addition, the differently stained regions and sub-regions are given numerical designations from proximal to distal on the chromosome arms. For example, Cri du chat syndrome involves a deletion on the short arm of chromosome 5. It is written as 46,XX,5p-. The critical region for this syndrome is deletion of p15.2 (the locus on the chromosome), which is written as 46,XX,del(5)(p15.2). [ 62 ]
Multicolor FISH and the older spectral karyotyping are molecular cytogenetic techniques used to simultaneously visualize all the pairs of chromosomes in an organism in different colors. Fluorescently labeled probes for each chromosome are made by labeling chromosome-specific DNA with different fluorophores . Because there are a limited number of spectrally distinct fluorophores, a combinatorial labeling method is used to generate many different colors. Fluorophore combinations are captured and analyzed by a fluorescence microscope using up to 7 narrow-banded fluorescence filters or, in the case of spectral karyotyping, by using an interferometer attached to a fluorescence microscope. In the case of an mFISH image, every combination of fluorochromes from the resulting original images is replaced by a pseudo color in a dedicated image analysis software. Thus, chromosomes or chromosome sections can be visualized and identified, allowing for the analysis of chromosomal rearrangements. [ 63 ] In the case of spectral karyotyping, image processing software assigns a pseudo color to each spectrally different combination, allowing the visualization of the individually colored chromosomes. [ 64 ]
Multicolor FISH is used to identify structural chromosome aberrations in cancer cells and other disease conditions when Giemsa banding or other techniques are not accurate enough.
Digital karyotyping is a technique used to quantify the DNA copy number on a genomic scale. Short sequences of DNA from specific loci all over the genome are isolated and enumerated. [ 65 ] This method is also known as virtual karyotyping . Using this technique, it is possible to detect small alterations in the human genome, that cannot be detected through methods employing metaphase chromosomes. Some loci deletions are known to be related to the development of cancer. Such deletions are found through digital karyotyping using the loci associated with cancer development. [ 66 ]
Chromosome abnormalities can be numerical, as in the presence of extra or missing chromosomes, or structural, as in derivative chromosome , translocations , inversions , large-scale deletions or duplications. Numerical abnormalities, also known as aneuploidy , often occur as a result of nondisjunction during meiosis in the formation of a gamete ; trisomies , in which three copies of a chromosome are present instead of the usual two, are common numerical abnormalities. Structural abnormalities often arise from errors in homologous recombination . Both types of abnormalities can occur in gametes and therefore will be present in all cells of an affected person's body, or they can occur during mitosis and give rise to a genetic mosaic individual who has some normal and some abnormal cells.
Chromosomal abnormalities that lead to disease in humans include
Some disorders arise from loss of just a piece of one chromosome, including
Chromosomes were first observed in plant cells by Carl Wilhelm von Nägeli in 1842. Their behavior in animal ( salamander ) cells was described by Walther Flemming , the discoverer of mitosis , in 1882. The name was coined by another German anatomist, Heinrich von Waldeyer in 1888. It is Neo-Latin from Ancient Greek κάρυον karyon , "kernel", "seed", or "nucleus", and τύπος typos , "general form")
The next stage took place after the development of genetics in the early 20th century, when it was appreciated that chromosomes (that can be observed by karyotype) were the carrier of genes. The term karyotype as defined by the phenotypic appearance of the somatic chromosomes, in contrast to their genic contents was introduced by Grigory Levitsky who worked with Lev Delaunay, Sergei Navashin , and Nikolai Vavilov . [ 67 ] [ 68 ] [ 69 ] [ 70 ] The subsequent history of the concept can be followed in the works of C. D. Darlington [ 71 ] and Michael JD White . [ 4 ] [ 13 ]
Investigation into the human karyotype took many years to settle the most basic question: how many chromosomes does a normal diploid human cell contain? [ 72 ] In 1912, Hans von Winiwarter reported 47 chromosomes in spermatogonia and 48 in oogonia , concluding an XX/XO sex determination mechanism. [ 73 ] Painter in 1922 was not certain whether the diploid of humans was 46 or 48, at first favoring 46, [ 74 ] but revised his opinion from 46 to 48, and he correctly insisted on humans having an XX/XY system. [ 75 ] Considering the techniques of the time, these results were remarkable.
Joe Hin Tjio working in Albert Levan 's lab [ 76 ] found the chromosome count to be 46 using new techniques available at the time:
The work took place in 1955, and was published in 1956. The karyotype of humans includes only 46 chromosomes. [ 77 ] [ 29 ] The other great apes have 48 chromosomes. Human chromosome 2 is now known to be a result of an end-to-end fusion of two ancestral ape chromosomes. [ 78 ] [ 79 ] | https://en.wikipedia.org/wiki/Karyotype |
Kasha's rule is a principle in the photochemistry of electronically excited molecules. The rule states that photon emission ( fluorescence or phosphorescence ) occurs in appreciable yield only from the lowest excited state of a given multiplicity . It is named after American spectroscopist Michael Kasha , who proposed it in 1950. [ 1 ] [ 2 ]
The rule is relevant in understanding the emission spectrum of an excited molecule. Upon absorbing a photon, a molecule in its electronic ground state (denoted S 0 , assuming a singlet state ) may – depending on the photon wavelength – be excited to any of a set of higher electronic states (denoted S n where n >0). However, according to Kasha's rule, photon emission (termed fluorescence in the case of an S state) is expected in appreciable yield only from the lowest excited state, S 1 . Since only one state is expected to yield emission, an equivalent statement of the rule is that the emission wavelength is independent of the excitation wavelength. [ 3 ]
The rule can be explained by the Franck–Condon factors for vibronic transitions . For a given pair of energy levels that differ in both vibrational and electronic quantum numbers , the Franck–Condon factor expresses the degree of overlap between their vibrational wavefunctions . The greater the overlap, the more quickly the molecule can undergo a transition from the higher to the lower level. Overlap between pairs is greatest when the two vibrational levels are close in energy; this tends to be the case when the vibrationless levels of the electronic states coupled by the transition (where the vibrational quantum number v is zero) are close. In most molecules, the vibrationless levels of the excited states all lie close together, so molecules in upper states quickly reach the lowest excited state, S 1 , before they have time to fluoresce. However, the energy gap between S 1 and S 0 is greater, so here fluorescence occurs, since it is now kinetically competitive with internal conversion (IC). [ 4 ] [ 5 ]
Exceptions to Kasha's rule arise when there are large energy gaps between excited states. An example is azulene : the classical explanation is that the S 1 and S 2 states lie sufficiently far apart that fluorescence is observed mostly from S 2 . [ 4 ] [ 5 ] In 2023, an explanation was proposed which pointed out that the S 1 excited state has antiaromatic character while the S 2 excited state is aromatic . [ 6 ]
A corollary of Kasha's rule is the Vavilov rule, which states that the quantum yield of luminescence is generally independent of the excitation wavelength. [ 4 ] [ 7 ] This can be understood as a consequence of the tendency – implied by Kasha's rule – for molecules in upper states to relax to the lowest excited state non-radiatively. Again there are exceptions: for example benzene vapour. [ 4 ] | https://en.wikipedia.org/wiki/Kasha's_rule |
Kashinhou (化審法), short for 化学物質の審査及び製造等の規制に関する法律 ( Kagaku Busshitsu no Shinsa Oyobi Seizoutou no Kisei ni Kansuru Houritsu ) , ("Law Concerning the Examination and Regulation of Manufacture, etc. of Chemical Substances") (Showa Act No. 117, 昭和48年法律第117号) is the current Chemicals and dangerous substances regulation law in Japan. The more concise abbreviated name is 化学物質審査規制法 ( Kagaku Busshitsu Shinsa Kiseihou ) , or "Chemical Substances Control Law". This law featured the world's first new chemical pre-examination system.
This law was established to provide a framework to examine the import, manufacture, and use of industrial chemicals and refractory organic substances for persistence and health consequences, as well as the necessary legal restrictions in order to achieve those aims.
The law has its origins in 1968, with an illness related to polychlorinated biphenyls poisoning in the Kanemi Oil Incident . In 1973, this law was established, radically overturning a prevailing attitude that long term contaminants bioaccumulating in humans was not problematic. Refractory organic substances, highly enriched uranium, and substances that possess long term toxicity to humans were classified as Section 1 Chemical Substances. Section 1 items were banned from manufacture or importation.
In 1986, a Section 2 Chemical Substances was added, which included trichloroethylene and tetrachloroethylene , which had contaminated groundwater. Questionable chemical substances that did not fall into above categories were introduced into a Section 2 Questionable Chemical substances category.
In 1999, the government ministries were reorganized, and the Ministry of the Environment was added as an overseer to the precursor ministries of the current Ministry of Health, Labour and Welfare , Ministry of Economy, Trade and Industry .
In 2003, under pressure from the Organisation for Economic Co-operation and Development , a third Section was created to surveillance of chemical substances harmful to flora and fauna but not to humans.
Regulation, policing, and surveillance of other laws, namely the Poisonous and Deleterious Substance Control Law, Stimulant Control Law, and Narcotics and Psychotropics Control Law were transferred to the current ministries as mentioned above.
[ 1 ] | https://en.wikipedia.org/wiki/Kashinhou |
The Kasner metric (developed by and named for the American mathematician Edward Kasner in 1921) [ 2 ] is an exact solution to Albert Einstein 's theory of general relativity . It describes an anisotropic universe without matter (i.e., it is a vacuum solution ). It can be written in any spacetime dimension D > 3 {\displaystyle D>3} and has strong connections with the study of gravitational chaos .
The metric in D > 3 {\displaystyle D>3} spacetime dimensions is
and contains D − 1 {\displaystyle D-1} constants p j {\displaystyle p_{j}} , called the Kasner exponents. The metric describes a spacetime whose equal-time slices are spatially flat, however space is expanding or contracting at different rates in different directions, depending on the values of the p j {\displaystyle p_{j}} . Test particles in this metric whose comoving coordinate differs by Δ x j {\displaystyle \Delta x^{j}} are separated by a physical distance t p j Δ x j {\displaystyle t^{p_{j}}\Delta x^{j}} .
The Kasner metric is an exact solution to Einstein's equations in vacuum when the Kasner exponents satisfy the following Kasner conditions,
The first condition defines a plane , the Kasner plane, and the second describes a sphere , the Kasner sphere. The solutions (choices of p j {\displaystyle p_{j}} ) satisfying the two conditions therefore lie on the sphere where the two intersect (sometimes confusingly also called the Kasner sphere). In D {\displaystyle D} spacetime dimensions, the space of solutions therefore lie on a D − 3 {\displaystyle D-3} dimensional sphere S D − 3 {\displaystyle S^{D-3}} .
There are several noticeable and unusual features of the Kasner solution: | https://en.wikipedia.org/wiki/Kasner_metric |
The Kastle–Meyer test is a presumptive blood test, first described in 1903, in which the chemical indicator phenolphthalein is used to detect the possible presence of hemoglobin . It relies on the peroxidase -like activity of hemoglobin in blood to catalyze the oxidation of phenolphthalin (the colorless reduced form of phenolphthalein) into phenolphthalein, which is visible as a bright pink color. The Kastle–Meyer test is a form of catalytic blood test, one of the two main classes of forensic tests commonly employed by crime labs in the chemical identification of blood. The other class of tests used for this purpose are microcrystal tests, such as the Teichmann crystal test and the Takayama crystal test. [ 1 ]
The test was named after the American agricultural chemist, Joseph Hoeing Kastle (1864–1916), who in 1901, invented and tested the crude blood test, and the German physician and chemist, Erich Meyer (1874–1927), who modified the test in 1903. [ 1 ]
In 1901, Joseph Hoeing Kastle and Oliver March Shedd in the U.S. found that biological material could cause the oxidation of phenolphthalin to phenolphthalein in slightly alkaline solutions. [ 2 ] In 1903, Erich Meyer in Germany found that blood cells could also trigger the reaction. [ 3 ] [ 4 ] In 1906, Kastle and Amoss found that chick hemoglobin in blood triggered the reaction. [ 5 ] In 1909, Kastle found that the test was sensitive to very dilute samples of blood. [ 6 ] However, in 1908, Pozzi-Escot (who by then was living in Lima, Peru) found that the test produced false positive reactions in response to a number of substances besides blood. [ 7 ] [ 8 ]
A presumed blood sample is first collected with a swab. A drop of phenolphthalein reagent is added to the sample, and after a few seconds, a drop of hydrogen peroxide is applied to the swab. If the swab turns pink rapidly, it is said to test presumptive positive for blood. Waiting for periods over 30 seconds will result in most swabs turning pink naturally as they oxidize on their own in the air. [ citation needed ]
Optionally, the swab can first be treated with a drop of ethanol in order to lyse the cells present and gain increased sensitivity and specificity. This test is nondestructive to the sample, which can be kept and used in further tests at the lab; however, few labs would use the swab used for the Kastle–Meyer test in any further testing, opting instead to use a fresh swab of the original stain. [ citation needed ]
While the Kastle–Meyer test has been reported as being able to detect blood dilutions down to 1:10 7 , there are a number of important limitations to the test. Chemical oxidants such as copper and nickel salts will cause the Kastle–Meyer reagent to turn pink before the addition of the hydrogen peroxide, thus it is vitally important to add the reagent first, then wait a few seconds, then add the hydrogen peroxide.
The Kastle–Meyer test has the same reaction with human blood as it does with any other hemoglobin-based blood, so a confirmatory test such as the Ouchterlony test must be performed to definitively conclude from which species the blood originated.
Color catalytic tests are very sensitive, but not specific. The positive color test alone should not be interpreted as positive proof of blood. A negative result is generally proof of the absence of detectable quantities of heme, however a false negative can be generated in the presence of a reducing agent. The test is unable to give specific evidence as to what is in the blood.
The phenolphthalein used in this test has been modified from its conventional form, in that it has been reduced by two electrons and is pre-dissolved in alkaline solution. This is typically achieved by boiling an alkaline solution of phenolphthalein with powdered zinc, which reduces the phenolphthalein into phenolphthalin. Upon reduction, the very intense pink color of the cationic form of phenolphthalein fades to a faint yellow color. It is this form of phenolphthalein that is present in Kastle–Meyer test kits. In order to generate the intense pink color indicative of a positive test, the reduced phenolphthalein must be oxidized back to its normal, colored form.
In the relevant reaction, hydrogen peroxide reacts with the hemoglobin in the blood. Phenolphthalein does not directly participate in this process; instead, it acts as an external source of electrons. In its reaction with hydrogen peroxide, the heme center of hemoglobin behaves as a peroxidase , reducing the peroxide to water. This activity depletes hemoglobin of electrons that are, in turn, re-supplied by the phenolphthalein. Donating electrons to hemoglobin converts the phenolphthalin back into the intensely colored phenolphthalein. As long as the enzyme survives, the reaction of heme with peroxide is catalytic , making this test very sensitive to small quantities of blood present on the test swab. The hemoglobin-catalyzed reduction of peroxide that occurs is shown in the reaction below. The two electrons are supplied by phenolphthalein:
The consumption of protons during the course of the reaction has the effect of raising the pH of the solution, but the amount of base produced is negligible compared to the amount of base already present in the reagent mixture. | https://en.wikipedia.org/wiki/Kastle–Meyer_test |
The katal (symbol: kat ) is a unit of the International System of Units (SI) [ 1 ] used for quantifying the catalytic activity of enzymes (that is, measuring the enzymatic activity level in enzyme catalysis ) and other catalysts. One katal is that catalytic activity that will raise the rate of conversion by one mole per second in a specified assay system. [ 1 ]
The unit "katal" is not attached to a specified measurement procedure or assay condition, but any given catalytic activity is: the value measured depends on experimental conditions that must be specified. [ 2 ] [ 3 ] Therefore, to define the quantity of a catalyst in katals, the catalysed rate of conversion (the rate of conversion in presence of the catalyst minus the rate of spontaneous conversion) of a defined chemical reaction is measured in moles per second. [ 4 ] One katal of trypsin , for example, is that amount of trypsin which breaks one mole of peptide bonds in one second under the associated specified conditions. [ clarification needed ]
One katal refers to an amount of enzyme that gives a catalysed rate of conversion of one mole per second . [ 5 ] [ 6 ] Because this is such a large unit for most enzymatic reactions, the nanokatal (nkat) is used in practice. [ 6 ]
The katal is not used to express the rate of a reaction ; that is expressed in units of concentration per second, as moles per liter per second. Rather, the katal is used to express catalytic activity, which is a property of the catalyst.
The General Conference on Weights and Measures and other international organizations recommend use of the katal. [ 7 ] It replaces the non-SI enzyme unit of catalytic activity. The enzyme unit is still more commonly used than the katal, [ 6 ] especially in biochemistry . [ citation needed ] [ 8 ] The adoption of the katal has been slow. [ 6 ] [ 9 ]
The name "katal" has been used for decades. The first proposal to make it an SI unit came in 1978, [ 6 ] [ 10 ] and it became an official SI unit in 1999. [ 6 ] [ 11 ] [ 12 ] The name comes from the Ancient Greek κατάλυσις ( katalysis ), meaning "dissolution"; [ 13 ] the word " catalysis " itself is a Latinized form of the Greek word. [ 13 ] [ 14 ] | https://en.wikipedia.org/wiki/Katal |
Katalin Balázsi (née Sedláčková ; born 1978) is a Slovakia-born Hungarian material scientist . She is the head of the Thin Film Physics department in the Institute of Technical Physics and Materials Science, a component of the Centre for Energy Research, Eötvös Lóránd Research Network. She has also served as the President of the Association of Hungarian Women in Science (2018-2021).
Balázsi was born in Šahy ( Ipolyság ), Slovakia in 1978. [ 1 ] While in elementary school, she represented her school in mathematics competitions. For high school, her father enrolled her in an electrician high school: there were four other girls in her class, and thirty-two boys. She graduated with the top ranking in her class. [ 2 ]
Balázsi completed her university degrees at the Faculty of Electrical Engineering and Information Technology of the Slovak University of Technology in Bratislava (STU). In 2000, she received a bachelor's degree in Electromaterials Engineering; she received a master's degree in materials science in 2002 from the same. [ 3 ] During her master's degree, Balázsi worked as a technician at the Slovak Academy of Sciences . She then became a researcher at the Academy, [ 2 ] using transmission electron microscopy to characterise the structures of nanomaterials; she received her doctorate in materials science from the STU in 2005. [ 4 ] The Institute of Electrical Engineering at the Academy named her the "Young Researcher". [ 3 ]
In 2006, Balázsi became a research fellow at the Institute of Technical Physics and Materials Science, part of the Hungarian Academy of Sciences . She was appointed as a senior scientist at the Institute's Centre for Energy Research in 2012. [ 3 ] Besides her work with electron microscopy, Balázsi has also studied the development of different ceramic materials. [ 5 ]
Balázsi and nine other female scientists founded the Association of Hungarian Women in Science in 2008 to address the national gender imbalance in Hungary's science sector; this Association won the first Nature Research Innovating Science Award in 2018. [ 6 ] [ 7 ] She has served as the Association's president from 2018 to 2021. [ 8 ] She also received the 2021 Acta Materialia Mary Fortune Global Diversity Medal. [ 3 ]
In 2021, she became the second Hungarian fellow of the European Ceramic Society (ECerS). [ 9 ] She is a board member of the European Platform of Women Scientists (EPWS). [ 10 ] She has also been secretary of the Hungarian Society for Material Sciences (2013-2020), as well as secretary and treasurer of the Hungarian Microscopic Society (2018-2022). [ 8 ]
Her husband Csaba Balázsi is also a scientist. They have two sons. [ 11 ] Besides Hungarian, she speaks Slovak, Czech, and English. [ 1 ] | https://en.wikipedia.org/wiki/Katalin_Balázsi |
Katalin Vesztergombi (born July 17, 1948) [ 1 ] is a Hungarian mathematician known for her contributions to graph theory and discrete geometry . A student of Vera T. Sós and a co-author of Paul Erdős , she is an emeritus associate professor at Eötvös Loránd University [ 2 ] and a member of the Hungarian Academy of Sciences . [ 3 ]
As a high-school student in the 1960s, Vesztergombi became part of a special class for gifted mathematics students at Fazekas Mihály Gimnázium with her future collaborators László Lovász , József Pelikán, and others. [ 4 ] She completed her Ph.D. in 1987 at Eötvös Loránd University . [ 1 ] [ 5 ] Her dissertation, Distribution of Distances in Finite Point Sets , is connected to the Erdős distinct distances problem and was supervised by Vera Sós. [ 5 ]
Vesztergombi's research contributions include works on permutations , [PR] graph coloring and graph products , [XN] combinatorial discrepancy theory , [SS] distance problems in discrete geometry , [LD] geometric graph theory , [GR] the rectilinear crossing number of the complete graph , [CQ] and graphons . [D1] [D2]
With László Lovász and József Pelikán, she is the author of the textbook Discrete Mathematics: Elementary and Beyond . [ 6 ] [DM]
Vesztergombi is married to László Lovász , with whom she is also a frequent research collaborator. [ 7 ] | https://en.wikipedia.org/wiki/Katalin_Vesztergombi |
Kaṭapayādi system ( Devanagari : कटपयादि, also known as Paralppēru , Malayalam: പരല്പ്പേര് ) of numerical notation is an ancient Indian alphasyllabic numeral system to depict letters to numerals for easy remembrance of numbers as words or verses . Assigning more than one letter to one numeral and nullifying certain other letters as valueless, this system provides the flexibility in forming meaningful words out of numbers which can be easily remembered.
The oldest available evidence of the use of Kaṭapayādi (Sanskrit: कटपयादि) system is from Grahacāraṇibandhana by Haridatta in 683 CE . [ 1 ] It has been used in Laghu·bhāskarīya·vivaraṇa written by Śaṅkara·nārāyaṇa in 869 CE . [ 2 ]
In some astronomical texts popular in Kerala planetary positions were encoded in the Kaṭapayādi system. The first such work is considered to be the Chandra-vakyani of Vararuci , who is traditionally assigned to the fourth century CE . Therefore, sometime in the early first millennium is a reasonable estimate for the origin of the Kaṭapayādi system. [ 3 ]
Aryabhata , in his treatise Ārya·bhaṭīya , is known to have used a similar, more complex system to represent astronomical numbers . There is no definitive evidence whether the Ka-ṭa-pa-yā-di system originated from Āryabhaṭa numeration . [ 4 ]
Almost all evidences of the use of Ka-ṭa-pa-yā-di system is from South India , especially Kerala . Not much is known about its use in North India. However, on a Sanskrit astrolabe discovered in North India , the degrees of the altitude are marked in the Kaṭapayādi system. It is preserved in the Sarasvati Bhavan Library of Sampurnanand Sanskrit University , Varanasi . [ 5 ]
The Ka-ṭa-pa-yā-di system is not confined to India. Some Pali chronograms based on the Ka-ṭa-pa-yā-di system have been discovered in Burma . [ 6 ]
Following verse found in Śaṅkaravarman's Sadratnamāla explains the mechanism of the system. [ 7 ] [ 8 ]
नञावचश्च शून्यानि संख्या: कटपयादय:। मिश्रे तूपान्त्यहल् संख्या न च चिन्त्यो हलस्वर:॥
Transliteration:
nanyāvachaścha śūnyāni sankhyāḥ kaṭapayādayaḥ miśre tūpāntyahal sankhyā na cha chintyo halasvaraḥ
Translation: na (न), ña (ञ) and a (अ)-s, i.e., vowels represent zero . The nine integers are represented by consonant group beginning with ka , ṭa , pa , ya . In a conjunct consonant, the last of the consonants alone will count. A consonant without a vowel is to be ignored.
Explanation: The assignment of letters to the numerals are as per the following arrangement (In Devanagari, Kannada, Telugu & Malayalam scripts respectively)
ఙ ങ
vyāsastadarddhaṃ tribhamaurvika syāt
This verse directly yields the decimal equivalent of pi divided by 10: pi/10 = 0.31415926535897932384626433832792
Traditionally, the order of digits are reversed to form the number, in katapayadi system. This rule is violated in this sloka.
The katapayadi scheme associates dha ↔ {\displaystyle \leftrightarrow } 9 and ra ↔ {\displaystyle \leftrightarrow } 2, hence the raga's melakarta number is 29 (92 reversed). 29 less than 36, hence Dheerasankarabharanam has Ma1. Divide 28 (1 less than 29) by 6, the quotient is 4 and the remainder 4. Therefore, this raga has Ri2, Ga3 (quotient is 4) and Da2, Ni3 (remainder is 4). Therefore, this raga's scale is Sa Ri2 Ga3 Ma1 Pa Da2 Ni3 SA .
From the coding scheme Ma ↔ {\displaystyle \leftrightarrow } 5, Cha ↔ {\displaystyle \leftrightarrow } 6. Hence the raga's melakarta number is 65 (56 reversed). 65 is greater than 36. So MechaKalyani has Ma2. Since the raga's number is greater than 36 subtract 36 from it. 65–36=29. 28 (1 less than 29) divided by 6: quotient=4, remainder=4. Ri2 Ga3 occurs. Da2 Ni3 occurs. So MechaKalyani has the notes Sa Ri2 Ga3 Ma2 Pa Da2 Ni3 SA .
As per the above calculation, we should get Sa ↔ {\displaystyle \leftrightarrow } 7, Ha ↔ {\displaystyle \leftrightarrow } 8 giving the number 87 instead of 57 for Simhendramadhyamam. This should be ideally Sa ↔ {\displaystyle \leftrightarrow } 7, Ma ↔ {\displaystyle \leftrightarrow } 5 giving the number 57. So it is believed that the name should be written as Sihmendramadhyamam (as in the case of Bra hm ana in Sanskrit).
Important dates were remembered by converting them using Kaṭapayādi system. These dates are generally represented as number of days since the start of Kali Yuga . It is sometimes called kalidina sankhya . | https://en.wikipedia.org/wiki/Katapayadi_system |
The Katchalski-Katzir algorithm is an algorithm for docking of rigid molecules, developed by Ephraim Katchalski-Katzir , Isaac Shariv and Miriam Eisenstein. [ 1 ] [ 2 ]
In 1990 Professor Ephraim Katchalski-Katzir, former president of the state of Israel, gathered a group of physicists, chemists and biologists at the Weizmann Institute of Science , to discuss intermolecular recognition. One of the outcomes of these discussions was the Katchalski-Katzir Algorithm, proposed by Dr. Isaac Shariv, a physics PhD student at the time. The Algorithm was implemented in a computer program, MolFit, by Dr. Miriam Eisenstein from the department of Structural Chemistry.
It is a purely geometric algorithm, but some extensions of it also implement electrostatics .
The algorithm's first step is mapping the molecules onto grids, with each point of a grid being marked as either:
The algorithm increases the surface contact and minimizes volume overlap. It is straightforward to compute such a score for a single alignment, but there are too many possible ways to align the molecules to simply iterate over them all.
To compute the scores for many alignments efficiently, fast Fourier transform (FFT) is applied to both grids. Having the grids in FFT form lets the scoring to be computed for many different alignments very quickly.
The Katchalski-Katzir algorithm is a fast but rather limited algorithm. It is usually used to quickly filter out the obviously wrong candidate structures. A structure may have good Katchalski-Katzir score (that is, fits well geometrically), but be a very bad fit overall, for example due to unfavourable electrostatic interactions or hydrophobic and hydrophilic groups facing each other. This is not a serious problem, as such structures can be filtered out later. A bigger issue is when a favourable structure is rejected by the algorithm. Some cases where this may happen include bad geometric fit being overcome by very strong attractive forces, or where the shape of the target changes because of the interactions ( induced fit ).
Programs that implement the Katchalski-Katzir algorithm include MolFit [ 3 ] and FTDock. [ 4 ]
This molecular modelling –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Katchalski-Katzir_algorithm |
Katharina Lodders is a German-American planetary scientist and cosmochemist who works as a research professor in the Department of Earth and Planetary Sciences at Washington University in St. Louis , where she co-directs the Planetary Chemistry Laboratory. [ 1 ] Her research concerns the chemical composition of solar and stellar environments, including the atmospheres of planets, exoplanets , and brown dwarfs , and the study of the temperatures at which elements condense in stellar environments. [ 2 ] [ 3 ]
Lodders completed her doctorate in 1991 at the University of Mainz , with research on the cosmochemistry of trace elements performed at the Max Planck Institute for Chemistry . [ 4 ] She joined Washington University in St. Louis as a postdoctoral researcher in 1992 before continuing there as a research professor. [ 2 ]
She served as a program director for galactic astronomy at the National Science Foundation from 2010 to 2013. [ 5 ]
Lodders is the coauthor of books including:
Lodders won the 2021 Leonard Medal of The Meteoritical Society , its highest award, "for her work on the condensation of presolar grains in stellar atmospheres and her compilation of the Solar System Abundances of the Elements and the condensation temperatures of the elements". [ 8 ] | https://en.wikipedia.org/wiki/Katharina_Lodders |
Katharine Hope Coward was a British pharmacologist and early adopter of chromatographic techniques. [ 1 ]
Coward was born on 2 July 1885 in Blackburn, Lancashire , England. She studied Botany and graduated M.Sc. from the University of Manchester . [ 2 ] After a few years, she joined University College London to study biochemistry and perform research under J. C. Drummond on Vitamin A, paving the way for her to be elected to a Fellow of the Chemical Society in 1923. [ 3 ]
In 1925, Coward received a Rockefeller Fellowship to continue her studies and research on vitamin A in the Department of Agricultural Chemistry at the University of Wisconsin–Madison under Dr. Harry Steenbock . On her return to Britain, she was appointed head of the Nutrition Department of the Royal Pharmaceutical Society 's pharmacological laboratories, in which position she remained until her retirement in 1950. [ 4 ] In 1937, she was elected as an honorary member of the Pharmaceuticals Society.
She was the "most prolifc woman contributor to the Biochemical Journal between 1906 and 1939". [ 5 ]
Because of her interest in nutrition and nutrients, Coward was one of the early adopters of chromatography following its introduction in 1906–1911 by Mikhail Tsvet .
Carotenoids , a class of structurally similar pigment molecules that include carotenes and xanthophylls , were of particular interest in nutritional research due to their demonstrated importance in animal studies. In his pioneering chromatographic research, Tsvet showed the presence of four different xanthophylls in his studies of plant extracts, separated through the use of adsorption chromatography . Following L. S. Palmer's descriptions of Tsvet's experiment in 1922, Coward replicated the methodology, the results of which she published in 1923. [ 6 ] During these studies Coward noted the presence of additional pigment (which would later be determined to be carotenes) in the eluent fractions, nearly developing a chromatographic method for the isolation of vitamin A from the carotenoids. This experiment made her the fifth scientist to adopt the use of chromatography, during a "dormant" period before the techniques popularization in the 1930s. [ 2 ]
This early research applying adsorption chromatography would continue in her role at the Royal Pharmaceutical Society, in conjunction with other analytical methods. [ 2 ]
Coward died at the age of 93 on 8 July 1978. [ 7 ] | https://en.wikipedia.org/wiki/Katharine_Coward |
Katherine Austin Lathrop (1915 – 2005) was an American nuclear medicine researcher, biochemist and member of the Manhattan Project . [ 1 ] [ 2 ] [ 3 ] [ 4 ]
Lathrop conducted pioneer work on the effects of radiation exposure on animals and humans.
Lathrop was born in Lawton, Oklahoma , on June 16, 1915. She attended Oklahoma A&M , where she earned bachelor's degrees in home economics and chemistry . She met her husband, Clarence Lathrop, while they were both studying for master's degrees in chemistry.. They married in 1938 and had five children.
Upon completion of their master's degrees in 1939, the couple first moved to New Mexico and then to Wyoming in 1941. Lathrop became a research assistant at the University of Wyoming where she focused her efforts on research pertaining to poisonous plants that grew on the Great Plains . In 1944, Lathrop and her family moved to Chicago where Clarence pursued a medical degree at Northwestern University . [ 5 ] They officially divorced in 1976.
Upon hearing her husband's friend talking about a secret project at the University of Chicago that hired scientists, she applied and was hired in the Biology Division of the Metallurgical Laboratory . Lathrop, who previously avoided work that involved animal experimentation , was now studying the uptake, retention, distribution, and excretion of radioactive materials in animals. Lathrop's assignment in the project was to test the biological effects radiation had on animals. She worked on the Manhattan Project from 1945 to 1946. [ 1 ] [ 5 ]
In 1947 after the Manhattan Project had been dismantled, Lathrop remained on staff at the lab as an associate biochemist as it was renamed Argonne National Laboratory . In 1954, tired of an exhausting commute, Lathrop left Argonne to pursue a career at the Argonne Cancer Research Hospital. It had opened in 1953 on the University of Chicago campus making it much closer to her home.
Lathrop was hired by the US Atomic Energy Commission facility as a research associate under the guidance of acclaimed researcher Paul Harper. Their goal was to find ways to manipulate radiation to allow for cancer detection and treatment. Their groundbreaking work on using the gamma camera to scan the body is a method still in practice to this day. The pair also discovered that Technetium 99-m could be used as a scanning agent.
She became a professor emeritus in 1985 and published her last paper in 1999 and then retired in 2000. [ 1 ] [ 4 ]
In addition to her research and teaching career, Lathrop was involved in national societies. In 1966, she helped establish the SNM Medical Internal Radiation Dose Committee. She also was the first person to teach radiation safety to workers that would come into contact with radioactive material. After semi-retirement, she became very involved with the Daughters of the American Revolution and genealogy . [ 1 ]
Lathrop retired in 2000 due to multiple cerebral ischemic attacks. She died in Las Cruces, New Mexico , on March 10, 2005, from complications caused by dementia .
Lathrop had five children. She had 10 grandchildren at the time of her death. [ 5 ] [ 6 ]
She died March 10, 2005. | https://en.wikipedia.org/wiki/Katherine_A._Lathrop |
Katherine Elkins is professor of humanities and comparative literature and faculty in Computing at Kenyon College .
Elkins attended Yale as an undergraduate, then completed a Ph.D. at UC Berkeley . She is the niece of Henry Elkins . [ citation needed ]
Elkins is a professor of comparative literature and humanities in the Integrated Program for Humane Studies (IPHS) [ 1 ] and faculty in Computing [ 2 ] at Kenyon College . She is a founding co-director of the KDH lab [ 3 ] and co-created the first human-centered artificial intelligence [ 4 ] curriculum launched in 2016 at Kenyon College [ 5 ] as the director of IPHS. She has mentored and co-authored hundreds of student ML/AI research projects in the humanities, arts and social sciences that have been downloaded almost 60,000 times worldwide as of September 2024. [ 6 ] Her recorded lectures with The Modern Scholar on The Modern Novel [ 7 ] (2021) and The Giants of French Literature [ 8 ] (2020) are tailored to broader public audiences via Amazon 's Audible.com . [ 9 ] She was nominated by graduating seniors to give the Kenyon College's December 2024 Baccalaureate Address which revisited David Foster Wallace's famous 2005 " This is Water " Kenyon graduation speech. [ 10 ]
Elkins is best known for her pioneering work on interdisciplinary artificial intelligence in literature , narrative , affective computing and the ethics of AI . Her book The S hapes of Stories, published by Cambridge University Press in 2022, [ 11 ] provided a comprehensive methodology for using diachronic sentiment analysis to analyze the emotional aspects of plot across dozens of literary classics using SentimentArcs. [ 12 ] This method has been used to analyze narrative in diverse forms including literature, [ 13 ] translations, [ 14 ] TV scripts, [ 15 ] end of life medical narratives, [ 16 ] and the evolution of social media narratives for elections [ 17 ] and economic crisis. [ 18 ]
She presented the first transdisciplinary AI research at leading academic conferences including the Modernist Studies Association in October 2019, [ 19 ] The International Society for the Study of Narrative in March 2020 [ 20 ] and the Modern Language Association Conference in January 2021. [ 21 ] Elkins was an early advocate for incorporating AI in literary studies with co-authored essays in The Journal of Cultural Analytics in September 2020 [ 22 ] and Narrative in January 2021. [ 23 ] More recently she focused on how AI redefines writing, [ 24 ] creativity, [ 25 ] authorship, [ 26 ] translations of literature, [ 27 ] eXplainable AI, [ 28 ] and the future of the academia in leading journals like Poetics Today . [ 29 ] Her article "A(I) University in Ruins: What Remains in a World with Large Language Models?" in the Proceedings of the Modern Language Association addresses how AI may fundamentally redefine traditional academic disciplines. [ 30 ] Her collaborative position paper addressing the risks and benefits of open-source AI was selected for oral presentation at ICML in July 2024. [ 31 ]
Elkins traditional scholarship includes essays on Plato , [ 32 ] Virginia Woolf , [ 33 ] Franz Kafka , [ 34 ] Marcel Proust , [ 35 ] and William Wordsworth . [ 36 ] In 2001 she won the A. Owen Aldridge Prize [ 37 ] in Comparative Literature for an essay on Charles Baudelaire . [ 37 ] She edited Philosophical Approaches to Proust’s In Search of Lost Time , which brings together essays by leading international Proust scholars, with Oxford University Press in 2022. [ 38 ]
Elkins is one of the leading women speaking widely on interdisciplinary AI. As early as 2019, she publicly advocated integrating AI into traditional humanities curriculum with a keynote address at the Ohio State University . [ 39 ] She gave the Meredith-Donovan lecture at Mount Saint Mary's University in 2023, [ 40 ] featured AI Working Group lecture at Wofford College , [ 41 ] and presentation at the Stories that Win Symposium at Washington University in 2024. [ 42 ] Elkins gives keynotes on the intersection of AI, digital humanities, education, and the future of work. Most recently, in the summer-fall of 2024, these included keynotes at Carleton College's Day of Digital Humanities , [ 43 ] Lafayette College AI Literacy Across the Curriculum, [ 44 ] and Austin College 's A.J. Carlson Lecture. [ 45 ] She will present on "How agentic behavior, reasoning, and emotional intelligence upend previous notions of human exceptionalism" for the Khan Institute at Smith College in February 2025. [ 46 ]
Elkins has been a co-panelist on interdisciplinary AI conversations with thought leaders from diverse fields. She discussed language, epistemology and the ethics of AI with Ned Block , Francesca Rossi , and Dennis Yi Tenen [ 47 ] in October 2022. [ 48 ] Elkins debated AI generative art with co-panelist Boris Eldagsen (winner [ 49 ] of Sony World Photography Award 2023) and Shane Balkowitsch on Al Jazeera in April 2023. [ 50 ] She presented her perspectives on emotions at the intersection of AI and literature with experts Rosalind Picard , Joseph LeDoux , and Mabel Berezin . [ 51 ] She discussed what gets lost in machine translation on the podcast Merging Minds. [ 52 ]
She is the AI industry expert for Bloomberg 's new AI Strategy Course [ 53 ] launched 2024. She serves as CAIO [ 54 ] of HumanCentricLabs [ 55 ] emphasizing humane applications of AI in the workplace.
Kenyon College awarded Elkins the senior trustee teaching award In 2014. [ 56 ] In March 2024 she was named a principal investigator for NIST 's US AI Safety Institute [ 57 ] representing the Modern Language Association . [ 58 ] She was awarded a Notre Dame - IBM Tech Ethics Lab [ 59 ] award in April 2024 to research the ethics and performance of SOTA LLM models to predict criminal recidivism. [ 60 ] Elkins has been a member of Meta 's Open Innovation AI Research Community [ 61 ] since 2023 and will present at the 2024 Conference at Meta's London Office in October. [ 62 ] In January 2025, Elkins presented her grant research finding on LLM predictive policing at Notre Dame. [1] | https://en.wikipedia.org/wiki/Katherine_Elkins |
Katherine Andrea Lemos is an American safety professional and the former chairperson and CEO of the U.S. Chemical Safety and Hazard Investigation Board (CSB).
Katherine Lemos was born to John Curtis and Laura Curtis. [ 2 ] Her father was a United States Air Force and Air National Guard pilot and a commercial airline pilot. [ 2 ] Lemos started flight lessons at the age of fourteen, at which time her father required her to read National Transportation Safety Board publications to learn about aviation safety and accidents. [ 2 ]
Lemos earned a B.B.A. in business management from Belmont University , a M.S. in behavioral counseling from California Lutheran University , and a Ph.D. in social psychology from University of Iowa . [ 3 ] [ 4 ] She also worked as a postdoctoral researcher at University of Iowa Operator Performance Laboratory and as a NASA Faculty Fellow at Langley Research Center . [ 5 ]
Lemos is a pilot and certified flight instructor. [ 4 ]
Prior to her appointment to CSB, Lemos worked at Northrop Grumman from 2014 to 2020, serving as the company's director of autonomy and director of programs for the aerospace sector. [ 6 ] She had previously worked as a technical leader and program manager for aviation safety at the Federal Aviation Administration and as an accident investigator and later Special Assistant to Vice Chairman of the Board of the National Transportation Safety Board . [ 3 ] [ 7 ] [ 8 ] She had also held academic positions at University of Maryland and Instituto Tecnológico de Aeronáutica . [ 9 ]
Lemos has specialized in system safety, accident investigation, and human factors. [ 1 ] [ 4 ] At the time she was nominated to CSB, she had no experience in chemical manufacturing or refinery operations, fields which fall under the purview of CSB investigation. [ 4 ]
Katherine Lemos was nominated by President Donald Trump to be a member of CSB on June 13, 2019. [ 3 ] [ 10 ] On July 22, she was nominated by President Trump to serve concurrent five-year appointments as chairperson and CEO of CSB. [ 3 ] [ 11 ] [ 12 ] At the time, the CSB's five-seat board had only three members, [ 13 ] one of whom would leave in December 2019. [ 2 ] The problem of vacancies in the CSB board was noted by a May 2019 Environmental Protection Agency Office of Inspector General report to be detrimental to CSB's ability to function effectively. [ 13 ] [ 14 ]
A hearing on her nomination was held by the United States Senate Committee on Environment and Public Works in September 2019. [ 2 ] Lemos received bipartisan support from committee members during her nomination. [ 4 ] Her appointment was confirmed by the Senate by unanimous consent on March 23, 2020. [ 12 ] [ 15 ] Senator John Barrasso said "it was critical the Senate confirm Dr. Lemos to provide a working quorum to the board"; [ 16 ] at the time of Lemos's confirmation, the CSB board had only one member, Kristen Kulinowski, [ 17 ] [ 6 ] and only eight investigators. [ 18 ] She began her tenure on April 23, 2020. [ 3 ]
Four days after Lemos's term began, Kulinowski announced that she would resign from CSB on May 1, ending the CSB's brief quorum. [ 19 ] At this time, CSB had ten unfilled investigator positions. [ 20 ] Thereafter, Lemos declared that she could operate as a "quorum of one", citing a legal opinion from the CSB general counsel allowing her to unilaterally run the CSB. [ 21 ] A July 2020 Environmental Protection Agency Office of Inspector General report concluded that it remained an open question whether a single CSB board member may constitute a quorum, as doing so would impair the segregation of duties mandated by the Government Accountability Office . [ 21 ] [ 22 ]
In May 2021, Public Employees for Environmental Responsibility criticized Lemos for accruing $33,000 in travel expenses and $20,000 in office renovations, and for hiring a senior advisor from Northrop Grumman for an undisclosed salary. [ 23 ] [ 24 ]
In a September 2021 hearing before the United States House Energy Subcommittee on Oversight and Investigations , Lemos testified that the CSB is "on an upward trend". [ 25 ] [ 26 ] She said that she intended to expand the staff of CSB to 61 people by September 2023. [ 18 ]
In September 2021, the Senate Committee on Environment and Public Works approved the nominations of three new board members of the CSB, [ 25 ] and in December 2021, two members were confirmed, Steve Owens and Sylvia Johnson . Once seated on the board in February 2022, Owens and Johnson openly disagreed with changes Lemos approved to a board order, which resulted in an expansion of the chairperson's authority. They attempted a procedural vote to make further changes to the order, but Lemos tabled the vote for a public meeting, which ultimately did not occur due to her resignation. [ 24 ]
Lemos submitted her letter of resignation to the White House in June 2022, citing lost confidence in the board's focus on the agency's mission. Her resignation became effective on July 22, 2022. [ 27 ]
In June 2023, the EPA Inspector General released a report stating that Lemos violated federal regulations for her use of board funds for travel, office refurbishment, and media training, but did not violate restrictions placed by a continuing resolution and did not violate regulations for the hiring of senior aides. [ 28 ] [ 29 ] Senator Chuck Grassley wrote a letter to Lemos requesting that she repay the money indicated as improperly spent in the report. [ 30 ] | https://en.wikipedia.org/wiki/Katherine_Lemos |
Kathleen Collen Gisser is an American chemist known for her work in film products and architectural paint . As a senior staff scientist at Sherwin Williams , Gisser led the team responsible for the development of the first EPA -registered microbicidal paint.
Kathleen ( née Collen) Gisser was born in Cleveland, Ohio , where she attended the Laurel High School in Shaker Heights . She later attended Yale University , where she double majored in classical civilization and chemistry. [ 1 ]
She went to the University of Wisconsin, Madison for graduate study in applied chemistry on metals and semiconductors, where she completed her Ph.D (1992) under the direction of Arthur B. Ellis , coauthoring several articles on nickel-titanium smart materials . [ 2 ] [ 3 ]
Gisser's first post following graduate school was at the Eastman Kodak Company [ 4 ] in Rochester, N.Y ., where her work focused on photographic/film technology. [ 1 ]
In the mid 1990s, Gisser had a role on the Kodak team that won a technical Oscar for a film product that fixed the "scratches and pops and dirt" on damaged copies of film reels. Gisser wrote the nomination for the award, and would later give a keynote at the American Chemical Society Presidential Event (1999), describing techniques related to this project. [ 5 ] [ 6 ]
In the second phase of her career Gisser moved to Sherwin-Williams, where her focus moved to the development of new paint technologies. Paint materials were being rapidly adapted during this period, with a shift towards recipes deemed be less toxic or significantly lower in volatile organic compounds simultaneous with a drive for new markets and "performance features." In 2015, Gisser's team at Sherwin-WIlliams was responsible for the development of Paint Shield®, the first EPA-registered microbicidal paint. [ 6 ] The CEO would tout the product as "one of the most significant technological breakthroughs in our nearly 150 year history of innovation." [ 7 ] At that time, paints with applications for reducing bacterial levels of Staph and MRSA , were regarded as desirable for use by healthcare and athletic facilities. "These types of inventions are desperately needed...to prevent transmission [of] resistant bacteria." [ 8 ] In subsequent years, use would be expanded "even [to] prefab military latrines." [ 1 ]
A Sherwin-Williams Research Fellow, [ 6 ] Gisser holds multiple patents in motion picture and photothermographic technology, [ 9 ] and is the recipient of awards at both the corporate and national level. These include: | https://en.wikipedia.org/wiki/Kathleen_Gisser |
Kathlyn Ann Parker is a chemist known for her work on synthesis of compounds, especially organic compounds with biological roles. She is an elected fellow of the American Chemical Society and a recipient of the Garvan–Olin Medal in chemistry.
Parker graduated from Senn High School in Chicago. [ 1 ] She went on to receive a B.A. from Northwestern University (1966). [ 2 ] While in college she won an award from the student chapter of the American Institute of Chemists for her essay "Chemistry as a Profession" making her the first woman to receive this award. [ 3 ] She earned her Ph.D. from Stanford University in 1970. [ 2 ] Following her Ph.D. she was a postdoctoral research at Columbia University . From 1973 until 2001 Parker was in the chemistry department at Brown University . [ 4 ] In 2001 she moved to Stony Brook University, [ 4 ] and in 2017 she was named a distinguished professor at Stony Brook University . [ 5 ]
Parker is known for her work in the field of organic synthesis , where she works on the construction of natural products through methods that allow for efficient synthesis of known organic compounds. [ 6 ]
In 1987 Parker was a fellow of the John Simon Guggenheim Foundation. [ 7 ] In 2009 the Parker was elected a fellow of the American Chemical Society and she received the Francis P. Garvan-John M. Olin Medal from the American Chemical Society. [ 2 ] [ 1 ] In 2017 she received the Arthur C. Cope Scholar Award in recognition of her work synthesizing organic compounds. [ 6 ]
This biographical article about a chemist is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kathlyn_A._Parker |
Kathryn Ann Moler (born c. 1966) is an American physicist , and current dean of research at Stanford University . [ 1 ] She received her BSc (1988) and Ph.D. (1995) from Stanford University . [ 2 ] After working as a visiting scientist at IBM T.J. Watson Research Center in 1995, she held a postdoctoral position at Princeton University from 1995 to 1998. She joined the faculty of Stanford University in 1998, and became an Associate in CIFAR 's Superconductivity Program (now called the Quantum Materials Program) in 2000. She became an associate professor (with tenure) at Stanford in 2002 and is currently a professor of applied physics and of Physics at Stanford. She currently works in the Geballe Laboratory for Advanced Materials (GLAM), [ 3 ] and is the director of the Center for Probing the Nanoscale (CPN), [ 4 ] a National Science Foundation-funded center where Stanford and IBM scientists continue to improve scanning probe methods for measuring, imaging, and controlling nanoscale phenomena. [ 5 ] She lists her scientific interests and main areas of research and experimentation as:
Early in her career, with John Kirtley from IBM, their research demonstrated that one of the predictions of a popular theory for high-temperature superconductivity was inaccurate by a factor of 10. [ 6 ] In 2011 her research group placed two non-magnetic materials (complex oxides) together and discovered an unexpected result: The layer where the two materials meet has both magnetic and superconducting regions. These are two properties that are normally incompatible, since "superconducting materials, which conduct electricity with no resistance and 100 percent efficiency, normally expel any magnetic field that comes near them." [ 7 ] Exploration of this phenomenon will be aimed toward discovery of whether the properties co-exist uneasily, or this marks the discovery of an exotic new form of superconductivity that actively interacts with magnetism.
In May 2018, Moler was named vice provost and dean of research at Stanford University, effective September 1, 2018. [ 8 ] | https://en.wikipedia.org/wiki/Kathryn_Moler |
Kato's conjecture is a mathematical problem named after mathematician Tosio Kato , of the University of California, Berkeley . Kato initially posed the problem in 1953. [ 1 ]
Kato asked whether the square roots of certain elliptic operators , defined via functional calculus , are analytic . The full statement of the conjecture as given by Auscher et al. is: "the domain of the square root of a uniformly complex elliptic operator L = − d i v ( A ∇ ) {\displaystyle L=-\mathrm {div} (A\nabla )} with bounded measurable coefficients in R n is the Sobolev space H 1 ( R n ) in any dimension with the estimate | | L f | | 2 ∼ | | ∇ f | | 2 {\displaystyle ||{\sqrt {L}}f||_{2}\sim ||\nabla f||_{2}} ". [ 2 ]
The problem remained unresolved for nearly a half-century, until in 2001 it was jointly solved in the affirmative by Pascal Auscher , Steve Hofmann , Michael Lacey , Alan McIntosh , and Philippe Tchamitchian . [ 2 ]
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kato's_conjecture |
In functional analysis , a subfield of mathematics, Kato's inequality is a distributional inequality for the Laplace operator or certain elliptic operators . It was proven in 1972 by the Japanese mathematician Tosio Kato . [ 1 ]
The original inequality is for some degenerate elliptic operators. [ 2 ] This article treats the special (but important) case for the Laplace operator. [ 3 ]
Let Ω ⊂ R d {\displaystyle \Omega \subset \mathbb {R} ^{d}} be a bounded and open set , and f ∈ L loc 1 ( Ω ) {\displaystyle f\in L_{\operatorname {loc} }^{1}(\Omega )} such that Δ f ∈ L loc 1 ( Ω ) {\displaystyle \Delta f\in L_{\operatorname {loc} }^{1}(\Omega )} . Then the following holds [ 4 ] [ 3 ]
where
L loc 1 {\displaystyle L_{\operatorname {loc} }^{1}} is the space of locally integrable functions – i.e., functions that are integrable on every compact subset of their domains of definition . | https://en.wikipedia.org/wiki/Kato's_inequality |
Katsumi Kaneko is a Japanese chemist and professor of Shinshu University.
He was born in Yokohama ( Kanagawa ), Japan . He graduated with a Bachelor of Engineering degree in 1969 from Yokohama National University (Applied Chemistry), Yokohama. He received a master's degree in physical chemistry at The University of Tokyo , in 1971. He received Doctor of Science in solid state chemistry in 1978 for submitted thesis from The University of Tokyo, entitled “Electrical Properties and Defect Structures of Iron Hydroxide Oxide Colloids” . [ 1 ]
He worked in Chiba University as a faculty of science until 2010, later he studied surface chemistry of metal hydroxide oxides and on gas adsorption, nanoporous materials, and nanospaces molecular science. Later, he became the dean of faculty of science and graduate school of science and technology of Chiba University. [ 2 ]
He is now a distinguished professor of Shinshu University since 2010. [ 3 ] [ 4 ]
He developed accurate characterization method of nanoscale pores with gas adsorption and established new nanospaces-molecular science; [ 5 ] he found unusual in-pore high pressure effect of nanoscale pores in which molecules and/or atoms prefer to form high pressure phase even without compression. One representative example of the in-pore high pressure effect is spontaneous formation of atomically 1D sulfur-chain of metallic property inside carbon nanotube under vacuum. Also he found partial dehydration of ions by confinement of ions in nanoscale pores, being essential to understand the supercapacitors. [ 6 ]
He gave a reasonable clue, cluster- associated hydrophobic-to-hydrophilic transformation, to understand water adsorption of nanoporous carbons of hydrophobicity hydration. [ 7 ] He contributed to understand adsorption of supercritical gases such as NO, CH 4 , and H 2 on nanoporous materials. He introduced the concept of quasi-vaporization of supercritical gases through an intensive molecule-pore interaction, giving an efficient guideline for improving adsorption of supercritical gases. [ 8 ] He has developed an efficient separation route of isotopic gases such as 18 O 2 and 16 O 2 . [ 9 ] He evidenced partial breaking of Coulombic law in electrically conductive carbon pores to induce association of cations or anions. He developed a sol-gel dispersant of single wall carbon nanotube, producing highly transparent conductive films and stretchable electrodes. [ 10 ]
He was awarded by Chemical Society of Japan in 1999 and the Charles Petinos Award by the American Carbon Society in 2007. He is fellow of Chemical Society of Japan since 2011, Royal Society of Chemistry and International Adsorption Society since 2013, [ 11 ] [ 12 ] and a Senior Member of the AIChE . [ 13 ] | https://en.wikipedia.org/wiki/Katsumi_Kaneko |
In mathematics , Katugampola fractional operators are integral operators that generalize the Riemann–Liouville and the Hadamard fractional operators into a unique form. [ 1 ] [ 2 ] [ 3 ] [ 4 ] The Katugampola fractional integral generalizes both the Riemann–Liouville fractional integral and the Hadamard fractional integral into a single form and It is also closely related to the Erdelyi–Kober [ 5 ] [ 6 ] [ 7 ] [ 8 ] operator that generalizes the Riemann–Liouville fractional integral. Katugampola fractional derivative [ 2 ] [ 3 ] [ 4 ] has been defined using the Katugampola fractional integral [ 3 ] and as with any other fractional differential operator , it also extends the possibility of taking real number powers or complex number powers of the integral and differential operators .
These operators have been defined on the following extended-Lebesgue space..
Let X c p ( a , b ) , c ∈ R , 1 ≤ p ≤ ∞ {\displaystyle {\textit {X}}_{c}^{p}(a,b),\;c\in \mathbb {R} ,\,1\leq p\leq \infty } be the space of those Lebesgue measurable functions f {\displaystyle f} on [ a , b ] {\displaystyle [a,b]} for which ‖ f ‖ X c p < ∞ {\displaystyle \|f\|_{{\textit {X}}_{c}^{p}}<\infty } , where the norm is defined by [ 1 ] ‖ f ‖ X c p = ( ∫ a b | t c f ( t ) | p d t t ) 1 / p < ∞ , {\displaystyle {\begin{aligned}\|f\|_{{\textit {X}}_{c}^{p}}=\left(\int _{a}^{b}|t^{c}f(t)|^{p}{\frac {dt}{t}}\right)^{1/p}<\infty ,\end{aligned}}} for 1 ≤ p < ∞ , c ∈ R {\displaystyle 1\leq p<\infty ,\,c\in \mathbb {R} } and for the case p = ∞ {\displaystyle p=\infty } ‖ f ‖ X c ∞ = ess sup a ≤ t ≤ b [ t c | f ( t ) | ] , ( c ∈ R ) . {\displaystyle {\begin{aligned}\|f\|_{{\textit {X}}_{c}^{\infty }}={\text{ess sup}}_{a\leq t\leq b}[t^{c}|f(t)|],\quad (c\in \mathbb {R} ).\end{aligned}}}
It is defined via the following integrals [ 1 ] [ 2 ] [ 9 ] [ 10 ] [ 11 ]
for x > a {\displaystyle x>a} and Re ( α ) > 0. {\displaystyle \operatorname {Re} (\alpha )>0.} This integral is called the left-sided fractional integral. Similarly, the right-sided fractional integral is defined by,
for x < b {\displaystyle \textstyle x<b} and Re ( α ) > 0 {\displaystyle \textstyle \operatorname {Re} (\alpha )>0} .
These are the fractional generalizations of the n {\displaystyle n} -fold left- and right-integrals of the form
and
respectively. Even though the integral operators in question are close resemblance of the famous Erdélyi–Kober operator , it is not possible to obtain the Hadamard fractional integrals as a direct consequence of the Erdélyi–Kober operators. Also, there is a corresponding fractional derivative, which generalizes the Riemann–Liouville and the Hadamard fractional derivatives . As with the case of fractional integrals, the same is not true for the Erdélyi–Kober operator.
As with the case of other fractional derivatives, it is defined via the Katugampola fractional integral. [ 3 ] [ 9 ] [ 10 ] [ 11 ]
Let α ∈ C , Re ( α ) ≥ 0 , n = [ Re ( α ) ] + 1 {\displaystyle \alpha \in \mathbb {C} ,\ \operatorname {Re} (\alpha )\geq 0,n=[\operatorname {Re} (\alpha )]+1} and ρ > 0. {\displaystyle \rho >0.} The generalized fractional derivatives, corresponding to the generalized fractional integrals ( 1 ) and ( 2 ) are defined, respectively, for 0 ≤ a < x < b ≤ ∞ {\displaystyle 0\leq a<x<b\leq \infty } , by
and
respectively, if the integrals exist.
These operators generalize the Riemann–Liouville and Hadamard fractional derivatives into a single form, while the Erdelyi–Kober fractional is a generalization of the Riemann–Liouville fractional derivative. [ 3 ] When, b = ∞ {\displaystyle b=\infty } , the fractional derivatives are referred to as Weyl-type derivatives.
There is a Caputo-type modification of the Katugampola derivative that is now known as the Caputo–Katugampola fractional derivative. [ 12 ] [ 13 ] Let f ∈ L 1 [ a , b ] , α ∈ ( 0 , 1 ] {\displaystyle f\in L^{1}[a,b],\alpha \in (0,1]} and ρ {\displaystyle \rho } . The C-K fractional derivative of order α {\displaystyle \alpha } of the function f : [ a , b ] → R , {\displaystyle f:[a,b]\rightarrow \mathbb {R} ,} with respect to parameter ρ {\displaystyle \rho } can be expressed as
It satisfies the following result. Assume that f ∈ C 1 [ a , b ] {\displaystyle f\in C^{1}[a,b]} , then the C-K derivative has the following equivalent form [ citation needed ]
Another recent generalization is the Hilfer-Katugampola fractional derivative. [ 14 ] [ 15 ] Let order 0 < α < 1 {\displaystyle 0<\alpha <1} and type 0 ≤ β ≤ 1 {\displaystyle 0\leq {\beta }\leq {1}} . The fractional derivative (left-sided/right-sided),
with respect to x {\displaystyle x} , with ρ > 0 {\displaystyle \rho >0} , is defined by
where δ ρ = t ρ − 1 d d t {\displaystyle \delta _{\rho }=t^{\rho -1}{\frac {d}{dt}}} , for functions φ {\displaystyle \varphi } in which the expression on the right hand side
exists, where J {\displaystyle {\mathcal {J}}} is the generalized fractional integral
given in ( 1 ).
As in the case of Laplace transforms , Mellin transforms will be used specially when solving differential equations . The Mellin transforms of the left-sided and right-sided versions of Katugampola Integral operators are given by [ 2 ] [ 4 ]
Let α ∈ C , Re ( α ) > 0 , {\displaystyle \alpha \in {\mathcal {C}},\ \operatorname {Re} (\alpha )>0,} and ρ > 0. {\displaystyle \rho >0.} Then, M ( ρ I a + α f ) ( s ) = Γ ( 1 − s ρ − α ) Γ ( 1 − s ρ ) ρ α M f ( s + α ρ ) , Re ( s / ρ + α ) < 1 , x > a , M ( ρ I b − α f ) ( s ) = Γ ( s ρ ) Γ ( s ρ + α ) ρ α M f ( s + α ρ ) , Re ( s / ρ ) > 0 , x < b , {\displaystyle {\begin{aligned}&{\mathcal {M}}{\bigg (}{}^{\rho }{\mathcal {I}}_{a+}^{\alpha }f{\bigg )}(s)={\frac {\Gamma {\big (}1-{\frac {s}{\rho }}-\alpha {\big )}}{\Gamma {\big (}1-{\frac {s}{\rho }}{\big )}\,\rho ^{\alpha }}}\,{\mathcal {M}}f(s+\alpha \rho ),\quad \operatorname {Re} (s/\rho +\alpha )<1,\,x>a,\\&{\mathcal {M}}{\bigg (}{}^{\rho }{\mathcal {I}}_{b-}^{\alpha }f{\bigg )}(s)={\frac {\Gamma {\big (}{\frac {s}{\rho }}{\big )}}{\Gamma {\big (}{\frac {s}{\rho }}+\alpha {\big )}\,\rho ^{\alpha }}}\,{\mathcal {M}}f(s+\alpha \rho ),\quad \operatorname {Re} (s/\rho )>0,\,x<b,\end{aligned}}}
for f ∈ X s + α ρ 1 ( R + ) {\displaystyle f\in {\textit {X}}_{s+\alpha \rho }^{1}(\mathbb {R} ^{+})} , if M f ( s + α ρ ) {\displaystyle {\mathcal {M}}f(s+\alpha \rho )} exists for s ∈ C {\displaystyle s\in \mathbb {C} } .
Katugampola operators satisfy the following Hermite-Hadamard type inequalities: [ 16 ]
Let α > 0 {\displaystyle \alpha >0} and ρ > 0 {\displaystyle \rho >0} . If f {\displaystyle f} is a convex function on [ a , b ] {\displaystyle [a,b]} , then f ( a + b 2 ) ≤ ρ α Γ ( α + 1 ) 4 ( b α − a α ) α [ ρ I a + α F ( b ) + ρ I b − α F ( a ) ] ≤ f ( a ) + f ( b ) 2 , {\displaystyle f\left({\frac {a+b}{2}}\right)\leq {\frac {\rho ^{\alpha }\Gamma (\alpha +1)}{4(b^{\alpha }-a^{\alpha })^{\alpha }}}\left[{}^{\rho }{\mathcal {I}}_{a+}^{\alpha }F(b)+{}^{\rho }{\mathcal {I}}_{b-}^{\alpha }F(a)\right]\leq {\frac {f(a)+f(b)}{2}},} where F ( x ) = f ( x ) + f ( a + b − x ) , x ∈ [ a , b ] {\displaystyle F(x)=f(x)+f(a+b-x),\;x\in [a,b]} .
When ρ → 0 + {\displaystyle \rho \rightarrow 0^{+}} , in the above result, the following Hadamard type inequality holds: [ 16 ]
Let α > 0 {\displaystyle \alpha >0} . If f {\displaystyle f} is a convex function on [ a , b ] {\displaystyle [a,b]} , then f ( a + b 2 ) ≤ Γ ( α + 1 ) 4 ( ln b a ) α [ I a + α F ( b ) + I b − α F ( a ) ] ≤ f ( a ) + f ( b ) 2 , {\displaystyle f\left({\frac {a+b}{2}}\right)\leq {\frac {\Gamma (\alpha +1)}{4\left(\ln {\frac {b}{a}}\right)^{\alpha }}}\left[\mathbf {I} _{a+}^{\alpha }F(b)+\mathbf {I} _{b-}^{\alpha }F(a)\right]\leq {\frac {f(a)+f(b)}{2}},} where I a + α {\displaystyle \mathbf {I} _{a+}^{\alpha }} and I b − α {\displaystyle \mathbf {I} _{b-}^{\alpha }} are left- and right-sided Hadamard fractional integrals .
These operators have been mentioned in the following works:
The CRONE (R) Toolbox, a Matlab and Simulink Toolbox dedicated to fractional calculus, can be downloaded at http://cronetoolbox.ims-bordeaux.fr | https://en.wikipedia.org/wiki/Katugampola_fractional_operators |
Katya Ravid is a Biochemistry and Cell Biology professor at Boston University Chobanian & Avedisian School of Medicine . [ 1 ] Ravid received her Bachelor of Science, PhD, and doctoral degree from the Israel Institute of Technology . She then received her postdoctoral at the Massachusetts Institute of Technology. [ 1 ] [ 2 ] As of 2021, she has been the inaugural incumbent of the Barbara E. Corkey Professor of Medicine of Boston University. [ 3 ] She's a member of the Boston University's Whitaker Cardiovascular Institute and the Boston University-Boston Medical Center (BU-BMC) Cancer Center. [ 4 ]
As a researcher in the fields of biochemistry and oncology, Ravid's research is focused on the study of blood platelets , adenosine receptors , and megakaryocytes to aid cancer patients. Her research allowed her to obtain multiple grants and become the founder of different programs for Boston University.
Boston University has recognized Ravid as being "nationally and internationally recognized" [ 3 ] for her discoveries, extensive research, and association to other programs. Under the university's announcement for title as the inaugural incumbent of the Barbara E. Corkey Professor of Medicine, one of the discoveries she was acclaimed for was her discovery of unique transcriptional signature that dictate how platelet lineage undergoes specification early in her career. [ 3 ]
Alongside her title of the inaugural incumbent of the Barbara E. Corkey Professor, she also became the founding director of the Evans Center for Interdisciplinary Biomedical Research in 2009. [ 5 ] The Evans Center for Interdisciplinary Biomedical Research is affiliated with the Evans Medical Foundation (founded in 1975) and the Department of Medicine at the Boston Medical Center (formally the Evans Department of Medicine). The Evans Center for Interdisciplinary Biomedical Research's goal is to establish a center in which faculty from the Department of Medicine and other schools can collaborate to promote biomedical research and education. [ 6 ]
Ravid is also the director for Boston University Interdisciplinary Biomedical Research Office (IBRO) that is funded by the Boston University's Office of Research and the Department of Medicine. Launched in 2015, the office seeks to foster and support different biomedical research programs in collaboration with faculty and other members of Boston University's medical center and the Charles River campuses (such as the Clinical Translational Science Institute). [ 7 ] [ 8 ]
She held the title of president for the Massachusetts Academy of Sciences (MAS) from 2018 to 2022. [ 4 ]
She has been a reporter/researcher for the National Institute of Health (NIH) since 2018. [ 9 ]
As an awardee of the American Heart Association 's Strategically Focused Research Network Award since 2021, she has received extensive funding and support from the association for her lab. She is the co-director of a lab focused on cancer-associated thromboembolism as affected by health disparities in collaboration with the American Heart Association. [ 10 ] [ 11 ] Her lab is one of three to have received the Strategically Focused Research Network Award to search for disparities in cardio oncology . The other labs that received the award are found at the University of Pennsylvania , Augusta University , and the Medical College of Wisconsin . Funding for these labs is planned to continue being provided until July 2025. [ 11 ]
News sources have highlighted Ravid's work for making new findings in the field of oncology. In 2021, Boston University's newspaper, The Brink , wrote about her research findings on the linkage between black cancer patients and their higher susceptibility to blood clots . [ 12 ] This was one of the findings in the lab funded by the American Heart Association. In 2021, The American Association for the Advancement of Science 's newsletter, EurekaAlert! , credited Dr. Ravid for her research and discovery of two drugs, PXS-LOX_1 and PXS-LOX_2, which can slow down the development of bone marrow cancer called primary myelofibrosis (PMF) . EurekaAlert! stated that "these drugs are unique because they are able to inhibit their target, a protein called lysyl oxidase , with a combination of specificity and potency not seen in previously tested drugs." [ 13 ]
2000-2005: She was awarded the Established Investigator Award by the American Heart Association. [ 9 ]
2011-2019: She was a vice chair and key speaker for the Gordon Research Conference in 2011, 2013, 2015, and 2019. Primarily for the cell biology of megakaryocytes and platelets section of the conference. [ 14 ] [ 15 ] [ 16 ] [ 17 ]
2014: She was elected as a fellow of the American Association for the Advancement of Science . [ 18 ]
2016: She was awarded the Fulbright Scholar Award and is the first biomedical researcher at Boston University to receive this award because of their extensive research on hematopoiesis and megakaryocytes. [ 19 ]
2019: She became a named member of the magazine, The American Society for Biochemistry and Molecular Biology. [ 20 ] | https://en.wikipedia.org/wiki/Katya_Ravid |
In number theory , the Katz–Lang finiteness theorem , proved by Nick Katz and Serge Lang ( 1981 ), states that if X is a smooth geometrically connected scheme of finite type over a field K that is finitely generated over the prime field , and Ker( X / K ) is the kernel of the maps between their abelianized fundamental groups , then Ker( X / K ) is finite if K has characteristic 0, and the part of the kernel coprime to p is finite if K has characteristic p > 0.
This number theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Katz–Lang_finiteness_theorem |
The Katětov–Tong insertion theorem [ 1 ] [ 2 ] [ 3 ] is a theorem of point-set topology proved independently by Miroslav Katětov and Hing Tong in the 1950s. The theorem states the following:
Let X {\displaystyle X} be a normal topological space and let g , h : X → R {\displaystyle g,h\colon X\to \mathbb {R} } be functions with g {\displaystyle g} upper semicontinuous , h {\displaystyle h} lower semicontinuous, and g ≤ h {\displaystyle g\leq h} . Then there exists a continuous function f : X → R {\displaystyle f\colon X\to \mathbb {R} } with g ≤ f ≤ h . {\displaystyle g\leq f\leq h.}
This theorem has a number of applications and is the first of many classical insertion theorems. In particular it implies the Tietze extension theorem and consequently Urysohn's lemma , and so the conclusion of the theorem is equivalent to normality. | https://en.wikipedia.org/wiki/Katětov–Tong_insertion_theorem |
In knot theory , the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman . [ 1 ] It is initially defined on a link diagram as
where w ( K ) {\displaystyle w(K)} is the writhe of the link diagram and L ( K ) {\displaystyle L(K)} is a polynomial in a and z defined on link diagrams by the following properties:
Here s {\displaystyle s} is a strand and s r {\displaystyle s_{r}} (resp. s ℓ {\displaystyle s_{\ell }} ) is the same strand with a right-handed (resp. left-handed) curl added (using a type I Reidemeister move).
Additionally L must satisfy Kauffman's skein relation :
The pictures represent the L polynomial of the diagrams which differ inside a disc as shown but are identical outside.
Kauffman showed that L exists and is a regular isotopy invariant of unoriented links. It follows easily that F is an ambient isotopy invariant of oriented links.
The Jones polynomial is a special case of the Kauffman polynomial, as the L polynomial specializes to the bracket polynomial . The Kauffman polynomial is related to Chern–Simons gauge theories for SO(N) in the same way that the HOMFLY polynomial is related to Chern–Simons gauge theories for SU(N). [ 2 ]
This knot theory-related article is a stub . You can help Wikipedia by expanding it .
This polynomial -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kauffman_polynomial |
The Kauffmann olefination is a chemical reaction to convert aldehydes and ketones to olefins with a terminal methylene group . This reaction was discovered by the German chemist Thomas Kauffmann and is related to the better known Tebbe olefination or Wittig reaction .
The reagent was generated in situ by conversion of different halogenides of molybdenum or tungsten with methyllithium at low temperatures (−78 °C). [ 1 ] [ 2 ] [ 3 ] [ 4 ]
During the warm-up process the formation of the active reagent occurs. NMR-experiments have shown that the active reagent is not a Schrock carbene (e.g. Tebbe-reagent).
Mechanism experiments shows that the olefination process is a sequence of cycloaddition and cycloelimination steps.
For a long time this reaction had no applications in synthetic organic chemistry. In 2002 it was used in a total synthesis of the terpene gleenol as a mild and non-basic reagent in a one-pot-protocol with an olefin metathesis step with Grubbs catalyst. [ 5 ] It is remarkable that the organometallic catalyst tolerates the inorganic reaction products. | https://en.wikipedia.org/wiki/Kauffmann_olefination |
Kausar Abdullah Malik (born 7 July 1945), [ 1 ] [ 2 ] is a noted agriculture scientist and educationist from Lahore , Punjab , Pakistan . [ 3 ]
Malik is the eldest son of noted Urdu language author, journalist and Marxist, Abdullah Malik . [ 4 ]
Malik attended Forman Christian College in Lahore , Pakistan from 1959–1961 and completed his Higher Secondary School Certificate . His Bachelor of Science and Master of Science are from Government College University, Lahore . He holds his Doctor of Philosophy in microbiology from Aston University , United Kingdom in 1970. [ 1 ]
Malik started his research career from the Nuclear Institute for Agriculture and Biology (NIAB), Faisalabad (1971-1992) ( Pakistan Atomic Energy Commission ). He is the founder Director General of the National Institute for Biotechnology and Genetic Engineering (NIBGE) at Faisalabad where he had been involved from the conceptual stage to its operation and developed all the research programs and scientific manpower. [ 1 ]
In view of his research and management experience, Dr Malik was appointed Chairman of the Pakistan Agricultural Research Council (PARC) which is the apex body responsible for coordinating research and development activities related to agriculture in the country (15 September 1998 – 27 February 2001). During his tenure he was able to establish an Agricultural Research Endowment Fund of Rs. 1.2 billion which is being utilized to fund competitive research grants in the country.
During 2001-2006, Malik served as Member (Biosciences & Administration) of the Pakistan Atomic Energy Commission and established Medical Institutes at different places in the country. Subsequently, he was invited to join Planning Commission (Pakistan) as its member looking after Food and Agriculture economic development from 2006-2008. During this period, Dr Malik also acted as the Secretary of the National Commission on Biotechnology (2002-2008). [ 1 ]
He has been awarded many prestigious awards by the Government of Pakistan on different occasions.
These are:
In 1997, he was awarded ISESCO Prize in Biology. [ 1 ] Malik is a Fellow of the Pakistan Academy of Sciences [ 1 ] and is one of five leading scientists and technologists appointed by the government to the Pakistan Council for Science and Technology. [ 6 ]
He is the Vice Chairman of National Technology Council (Pakistan) (NTC). [ 7 ] | https://en.wikipedia.org/wiki/Kauser_Abdullah_Malik |
In biophysics , the Kautsky effect (also fluorescence transient , fluorescence induction or fluorescence decay ) is a phenomenon consisting of a typical variation in the behavior of a plant fluorescence when exposed to light. It was discovered in 1931 by H. Kautsky and A. Hirsch.
When dark-adapted photosynthesising cells are illuminated with continuous light, chlorophyll fluorescence displays characteristic changes in intensity accompanying the induction of photosynthetic activity.
The quantum yield of photosynthesis, which is also the photochemical quenching of fluorescence, is calculated through the following equation:
Φ p = (F m -F 0 )/F m = F v /F m
F 0 is the low fluorescence intensity, which is measured by a short light flash that is not strong enough to cause photochemistry , and thus induces fluorescence. F m is the maximum fluorescence that can be obtained from a sample by measuring the highest intensity of fluorescence after a saturating flash. The difference between the measured values is the variable fluorescence F v .
When a sample (leaf or algal suspension) is illuminated, the fluorescence intensity increases with a time constant in the microsecond or millisecond range. After a few seconds the intensity decreases and reaches a steady-state level. The initial rise of the fluorescence intensity is attributed to the progressive saturation of the reaction centers of photosystem 2 (PSII). Therefore, photochemical quenching increases with the time of illumination, with a corresponding increase of the fluorescence intensity. The slow decrease of the fluorescence intensity at later times is caused, in addition to other processes, by non-photochemical quenching . Non-photochemical quenching is a protection mechanism in photosynthetic organisms as they have to avoid the adverse effect of excess light. Which components contribute and in which quantities remains an active but controversial area of research. It is known that carotenoids and the special pigment pairs (e.g. P700 ) have functions in photoprotection .
This biophysics -related article is a stub . You can help Wikipedia by expanding it .
This spectroscopy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kautsky_effect |
Kavka's toxin puzzle is a thought experiment about the possibility of forming an intention to perform an act which, following from reason, is an action one would not actually perform. It was presented by moral and political philosopher Gregory S. Kavka in "The Toxin Puzzle" (1983), and grew out of his work in deterrence theory and mutual assured destruction .
Kavka's original version of the puzzle is the following: [ 1 ]
An eccentric billionaire places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. All you have to do is ... intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin.
A possible interpretation: Can you intend to drink the toxin if you also intend to change your mind at a later time?
The paradoxical nature can be stated in many ways, which may be useful for understanding analysis proposed by philosophers:
Since the pain caused by the poison would be more than off-set by the money received, we can sketch the pay-off table as follows.
According to Kavka: Drinking the poison is never to your advantage regardless of whether you are paid. A rational person would know he would not drink the poison and thus could not intend to drink it.
David Gauthier argues once a person intends drinking the poison one cannot entertain ideas of not drinking it. [ 2 ]
The rational outcome of your deliberation tomorrow morning is the action that will be part of your life going as well as possible, subject to the constraint that it be compatible with your commitment—in this case, compatible with the sincere intention that you form today to drink the toxin. And so the rational action is to drink the toxin.
One of the central tenets of the puzzle is that for a reasonable person
Thus a reasonable person must intend to drink the toxin by the first argument, yet if that person intends to drink the toxin, he is being irrational by the second argument. | https://en.wikipedia.org/wiki/Kavka's_toxin_puzzle |
The Kavli Prize was established in 2005 as a joint venture of the Norwegian Academy of Science and Letters , the Norwegian Ministry of Education and Research , and the Kavli Foundation . It honors, supports, and recognizes scientists for outstanding work in the fields of astrophysics , nanoscience and neuroscience . Three prizes are awarded every second year. Each of the three Kavli Prizes consists of a gold medal, a scroll, and a cash award of US$1,000,000. The medal has a diameter of 70 millimetres (2.8 in), a thickness of 5 millimetres (0.20 in), and weighs 311 grams (11.0 oz). [ 1 ] [ 2 ]
The first Kavli Prizes were awarded on 9 September 2008 in Oslo , presented by Haakon, Crown Prince of Norway .
The Norwegian Academy of Science and Letters appoints three prize committees consisting of leading international scientists after receiving recommendations made from the following organisations: | https://en.wikipedia.org/wiki/Kavli_Prize |
Kazakh Leading Academy of Architecture and Civil Engineering ( Kazakh : Қазақ бас сәулет-құрылыс академиясы (ҚазБСҚА) , romanized : Qazaq bas säulet-qūrylys akademiiasy (QazBSQA) is a top institution among the higher education institutions of the Republic of Kazakhstan in fields of Architecture , Design , Civil Engineering , Environmental Engineering , Economics and Management in Construction.
The most important achievement and visible proof of international significance for the academy was accreditation of the study program of Architecture at KazGASA by UNESCO UIA Charter for Architectural Education. The certificate was awarded on 9 November 2007 and received by the academy in May 2008. It is the first higher education institution in the world accredited on "Architecture" major by UNIESCO UIA commission. [ citation needed ]
( KazGASA official website ) | https://en.wikipedia.org/wiki/Kazakh_Leading_Academy_of_Architecture_and_Civil_Engineering |
The Kazan Soda Elektrik , full name Kazan Soda Elektrik Üretim A.Ş ., is a chemical industry and electric energy company in Ankara Province , Turkey producing natural soda ash and baking soda from trona . The company is a subsidiary of Ciner Holding.
The trona ore deposits were owned by Rio Tinto Group , an Australian-British multinational and one of the world's largest metals and mining corporation. After survey activities, which lasted more than fifteen years, the company concluded that it will be unable to operate the mining of the trona ore reserves there, and sold the deposits to Ciner Holding in 2010. [ 1 ]
The construction of the soda products plant began in 2015, after five years of efforts for bureaucratic permissions and financing. The investment budget of the project was US$1.5 billion. [ 2 ] The financing of the project was provided by the Industrial and Commercial Bank of China (ICBC), Exim Bank of China and Deutsche Bank backed by the China Export and Credit Insurance Corporation (Sinosure). Sberbank of Russia financially contributed during the groundbreaking phase. [ 1 ] The construction of the facility was carried out by the China Tianchen Engineering Corporation (TCC). [ 3 ] [ 4 ] The facility was completed within two and half years. Kazan Soda Elektrik plant was inaugurated on January 15, 2018, in presence of Turkish President Recep Tayyip Erdoğan , Minister of Energy and Natural Resources Berat Albayrak , Minister of Labour and Social Security Jülide Sarıeroğlu , Ambassador of China Yu Hongyang and many other high-profile politicians and officials. [ 1 ]
The Kazan Soda Elektrik consists of three sections, namely mining, processing and cogeneration . [ 2 ] [ 5 ] While the mining area is located in Kahramankazan district, the production plant is situated within the Sincan district of Ankara Province, northwest of Ankara. [ 1 ] It is about 35 km (22 mi) north of Ankara . [ 5 ]
The plant's mining section supplies the processing section with the
trona solution ( trisodium hydrogendicarbonate dihydrat ), which is the primary source of soda ash. For this, trona ore, laying in average at a depth of 600 m (2,000 ft) underground, is injected with hot water through boreholes drilled, and the dissolved trona is pumped up in the form of trona solution. [ 2 ] The plant has five processing lines. [ 6 ] The congeneration facility produces 380 MWe electric power and 400 tons of steam. [ 7 ]
The annual production capacity of the plant is 2.5 million tons of soda ash ( sodium carbonate , Na 2 CO 3 ) and 200,000 tons of baking soda ( sodium bicarbonate , NaHCO 3 ). [ 2 ] If all the production were exported to Europe, it would increase the key glass raw material by around 25%. [ 6 ] Around 1,000 people are employed by the company. [ 2 ]
The trona ore reserve of Kazan Soda Elektrik is the world's second largest. [ 2 ] The plant is the biggest soda ash production facility in Europe. [ 2 ] With both Kazan Soda and Eti Soda, the Ciner Holding and Turkey becomes the leading soda ash producer of the world. The soda ash produced has a purity grade of 99.8%, which is the purest in the world. [ 1 ] The total annual export value of the products from Kazan Soda Elektrik and Eti Soda will be US$800 million. [ 1 ] [ 7 ]
The company has published a report by CDP scoring their environmental impact. [ 8 ] Their scope 1 and 2 emissions intensity in 2019 was 0.345 tonnes CO2e per tonne of product. [ 9 ] However, the first implementation of the EU Carbon Border Adjustment Mechanism does not include soda. [ 10 ] | https://en.wikipedia.org/wiki/Kazan_Soda_Elektrik |
In mathematics , a locally compact topological group G has property (T) if the trivial representation is an isolated point in its unitary dual equipped with the Fell topology . Informally, this means that if G acts unitarily on a Hilbert space and has "almost invariant vectors", then it has a nonzero invariant vector . The formal definition, introduced by David Kazhdan ( 1967 ), gives this a precise, quantitative meaning.
Although originally defined in terms of irreducible representations , property (T) can often be checked even when there is little or no explicit knowledge of the unitary dual. Property (T) has important applications to group representation theory , lattices in algebraic groups over local fields , ergodic theory , geometric group theory , expanders , operator algebras and the theory of networks .
Let G be a σ-compact, locally compact topological group and π : G → U ( H ) a unitary representation of G on a (complex) Hilbert space H . If ε > 0 and K is a compact subset of G , then a unit vector ξ in H is called an (ε, K )-invariant vector if
The following conditions on G are all equivalent to G having property (T) of Kazhdan , and any of them can be used as the definition of property (T).
(1) The trivial representation is an isolated point of the unitary dual of G with Fell topology .
(2) Any sequence of continuous positive definite functions on G converging to 1 uniformly on compact subsets , converges to 1 uniformly on G .
(3) Every unitary representation of G that has an (ε, K )-invariant unit vector for any ε > 0 and any compact subset K , has a non-zero invariant vector.
(4) There exists an ε > 0 and a compact subset K of G such that every unitary representation of G that has an (ε, K )-invariant unit vector, has a nonzero invariant vector.
(5) Every continuous affine isometric action of G on a real Hilbert space has a fixed point ( property (FH) ).
If H is a closed subgroup of G , the pair ( G , H ) is said to have relative property (T) of Margulis if there exists an ε > 0 and a compact subset K of G such that whenever a unitary representation of G has an (ε, K )-invariant unit vector, then it has a non-zero vector fixed by H .
Definition (4) evidently implies definition (3). To show the converse, let G be a locally compact group satisfying (3), assume by contradiction that for every K and ε there is a unitary representation that has a ( K , ε)-invariant unit vector and does not have an invariant vector. Look at the direct sum of all such representation and that will negate (4).
The equivalence of (4) and (5) (Property (FH)) is the Delorme-Guichardet theorem. The fact that (5) implies (4) requires the assumption that G is σ-compact (and locally compact) (Bekka et al., Theorem 2.12.4).
Examples of groups that do not have property (T) include
Historically property (T) was established for discrete groups Γ by embedding them as lattices in real or p-adic Lie groups with property (T). There are now several direct methods available. | https://en.wikipedia.org/wiki/Kazhdan's_property_(T) |
In the mathematical field of representation theory , a Kazhdan–Lusztig polynomial P y , w ( q ) {\displaystyle P_{y,w}(q)} is a member of a family of integral polynomials introduced by David Kazhdan and George Lusztig ( 1979 ). They are indexed by pairs of elements y , w of a Coxeter group W , which can in particular be the Weyl group of a Lie group .
In the spring of 1978 Kazhdan and Lusztig were studying Springer representations of the Weyl group of an algebraic group on ℓ {\displaystyle \ell } -adic cohomology groups related to conjugacy classes which are unipotent . They found a new construction of these representations over the complex numbers ( Kazhdan & Lusztig 1980a ). The representation had two natural bases, and the transition matrix between these two bases is essentially given by the Kazhdan–Lusztig polynomials. The actual Kazhdan–Lusztig construction of their polynomials is more elementary. Kazhdan and Lusztig used this to construct a canonical basis in the Hecke algebra of the Coxeter group and its representations.
In their first paper Kazhdan and Lusztig mentioned that their polynomials were related to the failure of local Poincaré duality for Schubert varieties . In Kazhdan & Lusztig (1980b) they reinterpreted this in terms of the intersection cohomology of Mark Goresky and Robert MacPherson , and gave another definition of such a basis in terms of the dimensions of certain intersection cohomology groups.
The two bases for the Springer representation reminded Kazhdan and Lusztig of the two bases for the Grothendieck group of certain infinite dimensional representations of semisimple Lie algebras, given by Verma modules and simple modules . This analogy, and the work of Jens Carsten Jantzen and Anthony Joseph relating primitive ideals of enveloping algebras to representations of Weyl groups, led to the Kazhdan–Lusztig conjectures.
Fix a Coxeter group W with generating set S , and write ℓ ( w ) {\displaystyle \ell (w)} for the length of an element w (the smallest length of an expression for w as a product of elements of S ). The Hecke algebra of W has a basis of elements T w {\displaystyle T_{w}} for w ∈ W {\displaystyle w\in W} over the ring Z [ q 1 / 2 , q − 1 / 2 ] {\displaystyle \mathbb {Z} [q^{1/2},q^{-1/2}]} , with multiplication defined by
The quadratic second relation implies that each generator T s is invertible in the Hecke algebra, with inverse T s −1 = q −1 T s + q −1 − 1 . These inverses satisfy the relation ( T s −1 + 1)( T s −1 − q −1 ) = 0 (obtained by multiplying the quadratic relation for T s by −T s −2 q −1 ), and also the braid relations . From this it follows that the Hecke algebra has an automorphism D that sends q 1/2 to q −1/2 and each T s to T s −1 . More generally one has D ( T w ) = T w − 1 − 1 {\displaystyle D(T_{w})=T_{w^{-1}}^{-1}} ; also D can be seen to be an involution.
The Kazhdan–Lusztig polynomials P yw ( q ) are indexed by a pair of elements y , w of W , and uniquely determined by the following properties.
To establish existence of the Kazhdan–Lusztig polynomials, Kazhdan and Lusztig gave a simple recursive procedure for computing the polynomials P yw ( q ) in terms of more elementary polynomials denoted R yw ( q ). defined by
They can be computed using the recursion relations
The Kazhdan–Lusztig polynomials can then be computed recursively using the relation
using the fact that the two terms on the left are polynomials in q 1/2 and q −1/2 without constant terms . These formulas are tiresome to use by hand for rank greater than about 3, but are well adapted for computers, and the only limit on computing Kazhdan–Lusztig polynomials with them is that for large rank the number of such polynomials exceeds the storage capacity of computers.
The Kazhdan–Lusztig polynomials arise as transition coefficients between their canonical basis and the natural basis of the Hecke algebra. The Inventiones paper also put forth two equivalent conjectures, known now as Kazhdan–Lusztig conjectures, which related the values of their polynomials at 1 with representations of complex semisimple Lie groups and Lie algebras , addressing a long-standing problem in representation theory.
Let W be a finite Weyl group . For each w ∈ W denote by M w be the Verma module of highest weight − w ( ρ ) − ρ where ρ is the half-sum of positive roots (or Weyl vector ), and let L w be its irreducible quotient, the simple highest weight module of highest weight − w ( ρ ) − ρ . Both M w and L w are locally-finite weight modules over the complex semisimple Lie algebra g with the Weyl group W , and therefore admit an algebraic character . Let us write ch( X ) for the character of a g -module X . The Kazhdan–Lusztig conjectures state:
where w 0 is the element of maximal length of the Weyl group.
These conjectures were proved over characteristic 0 algebraically closed fields independently by Alexander Beilinson and Joseph Bernstein ( 1981 ) and by Jean-Luc Brylinski and Masaki Kashiwara ( 1981 ). The methods introduced in the course of the proof have guided development of representation theory throughout the 1980s and 1990s, under the name geometric representation theory .
1. The two conjectures are known to be equivalent. Moreover, Borho–Jantzen's translation principle implies that w ( ρ ) − ρ can be replaced by w ( λ + ρ ) − ρ for any dominant integral weight λ . Thus, the Kazhdan–Lusztig conjectures describe the Jordan–Hölder multiplicities of Verma modules in any regular integral block of Bernstein–Gelfand–Gelfand category O .
2. A similar interpretation of all coefficients of Kazhdan–Lusztig polynomials follows from the Jantzen conjecture , which roughly says that individual coefficients of P y,w are multiplicities of L y in certain subquotient of the Verma module determined by a canonical filtration, the Jantzen filtration . The Jantzen conjecture in regular integral case was proved in a later paper of Beilinson and Bernstein ( 1993 ).
3. David Vogan showed as a consequence of the conjectures that
and that Ext j ( M y , L w ) vanishes if j + ℓ ( w ) + ℓ ( y ) is odd, so the dimensions of all such Ext groups in category O are determined in terms of coefficients of Kazhdan–Lusztig polynomials. This result demonstrates that all coefficients of the Kazhdan–Lusztig polynomials of a finite Weyl group are non-negative integers. However, positivity for the case of a finite Weyl group W was already known from the interpretation of coefficients of the Kazhdan–Lusztig polynomials as the dimensions of intersection cohomology groups, irrespective of the conjectures. Conversely, the relation between Kazhdan–Lusztig polynomials and the Ext groups theoretically can be used to prove the conjectures, although this approach to proving them turned out to be more difficult to carry out.
4. Some special cases of the Kazhdan–Lusztig conjectures are easy to verify. For example, M 1 is the antidominant Verma module, which is known to be simple. This means that M 1 = L 1 , establishing the second conjecture for w = 1, since the sum reduces to a single term. On the other hand, the first conjecture for w = w 0 follows from the Weyl character formula and the formula for the character of a Verma module , together with the fact that all Kazhdan–Lusztig polynomials P y , w 0 {\displaystyle P_{y,w_{0}}} are equal to 1.
5. Kashiwara (1990) proved a generalization of the Kazhdan–Lusztig conjectures to symmetrizable Kac–Moody algebras .
By the Bruhat decomposition the space G / B of the algebraic group G with Weyl group W is a disjoint union of affine spaces X w parameterized by elements w of W . The closures of these spaces X w are called Schubert varieties , and Kazhdan and Lusztig, following a suggestion of Deligne, showed how to express Kazhdan–Lusztig polynomials in terms of intersection cohomology groups of Schubert varieties.
More precisely, the Kazhdan–Lusztig polynomial P y , w ( q ) is equal to
where each term on the right means: take the complex IC of sheaves whose hyperhomology is the intersection homology of the Schubert variety of w (the closure of the cell X w ), take its cohomology of degree 2 i , and then take the dimension of the stalk of this sheaf at any point of the cell X y whose closure is the Schubert variety of y . The odd-dimensional cohomology groups do not appear in the sum because they are all zero.
This gave the first proof that all coefficients of Kazhdan–Lusztig polynomials for finite Weyl groups are non-negative integers.
Lusztig–Vogan polynomials (also called Kazhdan–Lusztig polynomials or Kazhdan–Lusztig–Vogan polynomials ) were introduced in Lusztig & Vogan (1983) . They are analogous to Kazhdan–Lusztig polynomials, but are tailored to representations of real semisimple Lie groups, and play major role in the conjectural description of their unitary duals . Their definition is more complicated, reflecting relative complexity of representations of real groups compared to complex groups.
The distinction, in the cases directly connection to representation theory, is explained on the level of double cosets ; or in other terms of actions on analogues of complex flag manifolds G / B where G is a complex Lie group and B a Borel subgroup . The original (K-L) case is then about the details of decomposing
a classical theme of the Bruhat decomposition , and before that of Schubert cells in a Grassmannian . The L-V case takes a real form G R of G , a maximal compact subgroup K R in that semisimple group G R , and makes the complexification K of K R . Then the relevant object of study is
In March 2007, a collaborative project, the "Atlas of Lie
groups and representations", announced that the L–V polynomials had been calculated for the split form of E 8 . [ 1 ]
The second paper of Kazhdan and Lusztig established a geometric setting for definition of Kazhdan–Lusztig polynomials, namely, the geometry of singularities of Schubert varieties in the flag variety . Much of the later work of Lusztig explored analogues of Kazhdan–Lusztig polynomials in the context of other natural singular algebraic varieties arising in representation theory, in particular, closures of nilpotent orbits and quiver varieties . It turned out that the representation theory of quantum groups , modular Lie algebras and affine Hecke algebras are all tightly controlled by appropriate analogues of Kazhdan–Lusztig polynomials. They admit an elementary description, but the deeper properties of these polynomials necessary for representation theory follow from sophisticated techniques of modern algebraic geometry and homological algebra , such as the use of intersection cohomology , perverse sheaves and Beilinson–Bernstein–Deligne decomposition .
The coefficients of the Kazhdan–Lusztig polynomials are conjectured to be the dimensions of some homomorphism spaces in Soergel's bimodule category. This is the only known positive interpretation of these coefficients for arbitrary Coxeter groups.
Combinatorial properties of Kazhdan–Lusztig polynomials and their generalizations are a topic of active current research. Given their significance in representation theory and algebraic geometry, attempts have been undertaken to develop the theory of Kazhdan–Lusztig polynomials in purely combinatorial fashion, relying to some extent on geometry, but without reference to intersection cohomology and other advanced techniques. This has led to exciting developments in algebraic combinatorics , such as pattern-avoidance phenomenon . Some references are given in the textbook of Björner & Brenti (2005) . A research monograph on the subject is Billey & Lakshmibai (2000) .
Kobayashi (2013) proved that values of Kazhdan–Lusztig polynomials at q = 1 {\displaystyle q=1} for crystallographic Coxeter groups satisfy certain strict inequality:
Let ( W , S ) {\displaystyle (W,S)} be a crystallographic Coxeter system
and P u w ( q ) {\displaystyle {P_{uw}(q)}} its Kazhdan–Lusztig polynomials.
If u < w {\displaystyle u<w} and P u w ( 1 ) > 1 {\displaystyle P_{uw}(1)>1} , then there exists a reflection t {\displaystyle t} such that P u w ( 1 ) > P t u , w ( 1 ) > 0 {\displaystyle P_{uw}(1)>P_{tu,w}(1)>0} . | https://en.wikipedia.org/wiki/Kazhdan–Lusztig_polynomial |
The KdpD/KdpE two-component system is a regulatory system involved in controlling potassium transport and intracellular osmolarity of pathogenic bacteria . [ 1 ] It plays an important role in potassium transport for osmoregulation of bacteria. In some bacteria, it can act as a virulence factor and acquire new adaptations from different selective pressures in the environment. [ 2 ] It is also demonstrated to maintain internal pH, stress responses, enzyme activation , and gene expression . [ 3 ] K+ ions are used for necessary biological processes and can generate a negative electric potential on the cytoplasmic side of the plasma membrane. [ 4 ] There are different uptake systems for K+ ions, but the specific mechanisms vary between species.
The KdpD/KdpE system is mainly responsible for the regulation of potassium concentrations within the cell to maintain homeostasis . This system is induced and repressed by quorum molecules, nutrient levels, pH , and ATP concentrations. [ 2 ] It can be triggered when there is a lack of potassium ions in the cell, which may be sensed by a decrease in turgor pressure. Interestingly, the kdpFABC gene is reportedly only activated by salts and not sugar, despite both of them increasing osmolarity. [ 5 ] This system has a higher affinity for potassium ions compared to average potassium pumps.
The KdpD/KdpE system can contribute to an organism's virulence factor and aid in longer survival. In a study, they examined a strain of avian pathogenic E.coli , AE17ΔKdpDE, and created deletion mutants that affected the KdpD/KdpE system. They found that the deletion mutants, when compared to the WT, had decreased motility, fewer flagellum , altered metabolic pathways, and assembly of movement mechanisms. Since the deletion mutant's motility was significantly underdeveloped, it majorly decreased the virulence of the avian E.coli. [ 6 ] Another study inserted the KdpD/KdpE system gene from Photorhadbus asymbiotica into E. coli via a transposition, which resulted in E. coli being able to evade the host cells and not perish by phagocytosis . [ 7 ]
KdpD, a sensor kinase , is sensitive to changes in extracellular concentrations of potassium. KdpD is a homodimer consisting of four transmembrane domains , an N-terminal cytoplasmic domain, and a C-terminal cytoplasmic domain. KdpD possesses autokinase, phosphotransferase , and protein phosphatase activity. KdpD undergoes autophosphorylation due to fluctuations in the concentration of potassium. The phosphorylated KdpD-P activates KdpE. [ 2 ]
KdpE, a transcriptional regulator , regulates the expression of genes containing high-affinity potassium transport systems. [ 8 ] KdpE is a cytoplasmic, homodimer protein. [ 9 ] KdpE is phosphorylated by KdpD-P. The activated KdpE-P, a transcription factor, binds to the kdpFABC operon encoding high-affinity potassium transporters. [ 2 ]
The early models of KdpD stimulus proposed that KdpD sensed changes in turgor pressure. It was later found that the intracellular concentration of potassium affects the autophosphorylation of KdpD. High concentrations of intracellular potassium inhibit the autophosphorylation of KdpD. KdpD also detects changes in intracellular ionic strength. Higher concentrations of extracellular salts stimulate KdpD phosphorylation. The N-terminal domain contains two parts (Walker A & B) that act as ATP binding sites. The intracellular level of ATP affects the autophosphorylation of KdpD. Accessory proteins like UspC, act as scaffolding proteins during salt stress. UspC belongs to a family of scaffolding proteins called universal stress proteins. UspC stabilizes the KdpD/KdpE complex during phosphotransferase activity. [ 10 ]
The activated KdpE-P acts as a transcriptional activator by attaching to the operon of the kdpFABC gene. The resulting KdpFABC complex is a high-affinity potassium P-Type ATPase. This ATPase transports potassium intracellularly against the electrochemical gradient using ATP. [ 11 ] The KdpF subunit stabilizes the transport complex. [ 12 ] The KdpA subunit is responsible for the binding and translocation of potassium ions. [ 13 ] The KdpB subunit is responsible for the hydrolysis of ATP to provide energy for translocation. [ 14 ] The KdpC subunit is an inner membrane protein with no known function. [ 15 ] [ 16 ]
KdpD/KdpE two-component system (TCS) is something that can be found in many bacteria genera/species. A few examples of bacteria that use this system are Escherichia coli, Staphylococcus aureus, and Mycobacterium.
KdpD/KdpE is a TCS system that is found in Escherichia coli and produces K+ transporter Kdp-ATPase. This TCS system was characterized first in the bacterial species of E. coli . [ 17 ] The transporter is used as a scavenging system for K+ when it is extremely limited. The TCS system for E. coli has four distinct proteins from one single operon, kdpFABC. The element that regulates the TCS is KdpD/E and is located downstream from the gene KdpC. When there is a K+ limitation, typically from an added salt, KdpD histidine kinase autophosphorylation and the response regulator, KdpE, receive the phosphoryl group . After which affinity increases by 23 base pairs in the sequence upstream from the promoter kdpFABC triggers transcription. This system is used in many gram-negative and gram-positive bacteria.
Currently, KdpD/E is a TCS found in Staphylococcus aureus . This shows repression on transcription for kdpFABC. This happens in all conditions of K+ and brings to attention that KdpFABC is not a major transporter for K+. [ 18 ] When KdpD/E becomes inactivated transcription becomes altered for virulence genes. This alteration can affect many different genes including, but not limited to Spa, geh, hla, etc. KdpE binds directly to promoter regions of these genes to regulate transcription for them. KdpD/E transcript levels can be directly related to K+ concentration externally. The S. aureus can modulate infection status by using K+ external stimuli from the environment. The transcript level of KdpD/E can also become activated by Agr/RNAIII when in the post-exponential phase which was confirmed through Rot.
Kdp system is found in many different Mycobacterium species including M. tuberculosis , M. avium , M. bovis , M. smegmatis , M. marinum , and others. [ 19 ] The Kdp although is not contained within the M. leprae and M. ulcerans spp . The KdpD/KdpE TCS is not a well-characterized system for the spp. smegmatis because there are many different types of TCS in many different types of Mycobacterium spp . The KdpD/KdpE is a TCS in Mycobacterial species that can regulate potassium homeostasis, regulation mechanism and function for target genes that are located downstream that help with infections from Mycobacteria . The system could be a target for antibiotic resistance for the mycobacterial infection because the major differences within the potassium uptake systems of eukaryotes and prokaryotes . In these spp. the KdpE binds to the promoter region for kdpFABC operon (PkdpF) and KdpF coding sequence for Mycobacteria is found.
The KdpD/KdpE system is often altered for genetic experiments in virulence and pathogenicity. For example, an experiment took the genes for the KdpD/KdpE system and inserted them into avian pathogenic E.coli cells using a transposon and compared them to an unaltered group. The insertion mutants were less likely to be killed via phagocytosis and had an effect on the cells' metabolism, global transcription, and flagellar assembly. [ 7 ] In another study, the genes of the KdpD/KdpE system from Photorhabdus asymbiotica were put into a lab strain of E.coli via a transposon. They observed that the previously susceptible E.coli strain was now able to resist phagocytic killing and longer persist against host cells. [ 6 ] | https://en.wikipedia.org/wiki/KdpD/KdpE_two-component_system |
Ke Kā o Makaliʻi ( lit. ' The Canoe-Bailer of Makali‘i ' ) is a Hawaiian constellation consisting of five stars in a curving formation in the shape of a bailer surrounding the western constellation Orion , although not including any stars from it. The constellation is seen to rise in the east like a cup and set in the west pouring onto the western horizon. [ 1 ] [ 2 ]
Ke Kā o Makali‘i comprises five stars:
This constellation -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ke_Kā_o_Makaliʻi |
Kê T'ing-sui or Ge Tingsui ( Chinese : 葛庭燧 ; pinyin : Gê Tíngsùi ; Wade–Giles : Kê T'íng-suì ; May 3, 1913 – April 29, 2000), also known as T.S. Kê , was a Chinese physicist and writer renowned for his contributions in internal friction , anelasticity, solid state physics and metallurgy . He was the member of the Chinese Academy of Sciences , known for the Kê-type pendulum and Kê grain-boundary internal friction peak named after him. In March 1982, he founded the Institute of Solid State Physics in Hefei , Anhui , China .
Kê was born in Penglai , Shandong province. He was admitted to Tsinghua University in 1930 but suffered pulmonary disease which required him to rest for two years where he earned a B.S. in physics in 1937. He obtained an M.S. in physics at Yenching University in 1940. In July 1941, Kê married He Yizhen in Shanghai and the following month they traveled together to California. Kê received his Ph.D. in physics after only pursuing it for two years at the University of California at Berkeley in 1943. [ 2 ] In the years 1943–1945 and 1945–1949, respectively, he worked as a staff member at the Massachusetts Institute of Technology and research associate at the University of Chicago.
In 1949, Kê returned to China and became a professor in physics at Tsinghua University and a research associate at the Applied Physics Laboratory of the Chinese Academy of Sciences (CAS). In October 1952, he relocated to Shenyang to participate in the establishment of the Institute of Metal Research of CAS as a research associate where he became deputy director from 1961 to 1981. In 1955, Kê was elected academician of CAS and became a member of the Mathematics and Physics Committee of CAS. In 1980, he was transferred to Hefei for the establishment of the Hefei branch of CAS where he served as its deputy director and later jointly became the first head of the Institute of Solid State Physics incepted in March 1982.
In 1979 he was a visiting professor at the Max-Planck Institut für Metallforschung in Germany, and in 1980, a guest professor at the INSA de Lyon in France.
In 1945, Kê started research on internal friction and anelastic properties in metals at the University of Chicago where he accomplished advanced studies of grain-boundary relaxation and non-linear anelastic relaxation associated to interactions between point defects and dislocations. This work continued after he returned to China in 1949 where he made further progress. The Kê-type torsion pendulum bears his name, [ 3 ] as well as the Kê grain-boundary internal friction peak. [ 4 ] Kê also proposed the Kê grain-boundary model for disordered atomic groups. Kê also participated in the Manhattan Project and the Long-Range Radar projects.
In 1941, Kê married He Yizhen , a physicist who would specialize in amorphous physics was metallic glass, and was a founder of the Institute of Metal Research and Institute of Solid State Physics. They developed a competitive relationship with one another due to their studies in the same field.
The couple met at Yenching University, where he had been a lecturer and was three years older than Kê. Because He came from a wealthy and influential family, she had a number of admirers; her family did not approve of her relationship with Kê became he came from a poor family and also suffered from pulmonary tuberculosis , for which a valid treatment was not available at the time. Furthermore, Kê's political beliefs clashed with He's father, who disagreed with Ge's support of the political activism of students. In opposition to her family's wishes, she married Kê; their marriage became a much-told tale in Chinese academia and their love letters are still preserved in their biographies. [ 5 ]
After their marriage, Kê obtained the opportunity to study in the United States with He, where they remained from 1941 to 1949. Their two children were born in the United States and eventually became scientists: their daughter Ge Yunpei (1942-2013) was a professor in Shenyang Jianzhu University , while their son Ge Yunjian (born 1947), is an expert in robotics. The couple returned to China in 1949, where they both worked for the Chinese Academy of Science for decades. When Kê was dispatched to work in Hefei in 1980, Kê and their children persuaded He to stop her research to join him in Hefei.
Professor T.S. Kê was a recipient of numerous national and international awards such as the Zener Prize [ 6 ] in 1989, and Robert Franklin Mehl Award in 1999 (considered to be the highest international award in the field of materials science). [ 7 ] | https://en.wikipedia.org/wiki/Ke_T'ing-sui |
In physics , The Keating Model is a model that theoretical physicist Patrick N. Keating introduced in 1966 to describe forces induced on neighboring atoms when one atom moves in a solid.
The term most often applies to the forces on first- and second-nearest neighboring atoms that arise when an atom is moved in tetrahedrally -bonded solids , such as diamond , silicon , germanium , and a number of other covalent crystals with the diamond or zinc blende structures.
Crystalline solids generally consist of an ordered array of interconnected atoms, generated by repetition of a unit cell in three dimensions, and are of two extreme types—ionic crystals, and covalent crystals. Others are intermediate: partly ionic and partly covalent. Ionic crystals are made up of quite different ions, such as Na + and Cl − in common salt, for example, while covalent crystals such as diamond are made up of atoms that share electrons in a covalent bond .
In either case, attractive and repulsive forces resist moving an atom/ion or a set of them from their equilibrium positions, thus giving solids their rigidity against compressive, tensile, and shear stresses . The nature and strength of these forces is important for the scientific understanding of solids since they determine the way the solid responds to these stresses (elastic constants), the velocity of sound waves in it, its infra-red absorption, and many other properties.
The Keating model is the result of a general method proposed to ensure that the elastic strain energy satisfies the requirement that it is invariant under a simple rotation of the crystal, without deformation . It is a formalism for the way adjacent and close-by atoms respond when one or more atoms move in covalently bonded crystals. It is also a specific parameterization of this response for diamond, silicon, and germanium. (see the article listed under "Further Reading").
The general method is applicable for small atomic displacements to all crystal structures. [ 1 ] [ 2 ] It has been extended by P. N. Keating to include anharmonic effects (and calculate third-order elastic constants), [ 3 ] and many other researchers have extended it to include forces between the covalent bonds, and augment it in other ways.
The key paper that introduced the model was one of the 50 highest-impact papers over a century of Physical Review publications [1] ). The model has been, and is, used by many research scientists for calculating elastic constants, lattice dynamics, band structure , dislocation strains, atomic configurations at surfaces and interfaces, and other purposes for a wide range of solids, including amorphous (i.e., non-crystalline) materials. | https://en.wikipedia.org/wiki/Keating_model |
Keatite is a silicate mineral with the chemical formula Si O 2 ( silicon dioxide ) that was discovered in nature in 2013. It is a tetragonal polymorph of silica first known as a synthetic phase. [ 1 ] It was reported as minute inclusions within clinopyroxene ( diopside ) crystals in an ultra high pressure garnet pyroxenite body. The host rock is part of the Kokchetav Massif in Kazakhstan . [ 2 ]
Keatite was synthesized in 1954 and named for Paul P. Keat who discovered it while studying the role of soda in the crystallization of amorphous silica . [ 3 ] Keatite was well known before 1970 as evidenced in few studies from that era. [ 4 ] [ 5 ]
This article about a specific silicate mineral is a stub . You can help Wikipedia by expanding it .
This article about materials science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Keatite |
In organic chemistry , the Keck asymmetric allylation is a chemical reaction that involves the nucleophilic addition of an allyl group to an aldehyde. The catalyst is a chiral complex that contains titanium as a Lewis acid . The chirality of the catalyst induces a stereoselective addition, so the secondary alcohol of the product has a predictable absolute stereochemistry based on the choice of catalyst. This name reaction is named for Gary Keck .
The Keck asymmetric allylation has many applications to the synthesis of natural products , [ 1 ] including (−)-Gloeosporone, [ 2 ] Epothilone A, [ 3 ] the CD-Subunit of spongistatins, [ 4 ] and the C10-C20 Subunit of rhizoxin A, [ 5 ] The Keck allylation has also been utilized to form substituted tetrahydropyrans enantioselectively, moieties found in products such as phorboxazole and bryostatin 1. [ 6 ]
Although the groups of E. Tagliavini [ who? ] and K. Mikami [ who? ] reported the catalysis of this reaction using a Ti(IV)–BINOL complex in the same year as the Keck group, [ 7 ] [ 8 ] Keck's publication reported higher enantio- and diastereoselectivity, and did not require the use of 4 Angstrom molecular sieves as in Mikami's procedure or an excess of BINOL as in Tagliavini's procedure. [ 9 ]
Keck's early success with stereoselectivity and the simplicity of the catalyst preparation led to many improvements in reaction design, including development of other structural analogs of BINOL, use of stoichiometric additives to enhance the reaction rate, and broadening the scope of the reaction to include substituted stannane nucleophiles.
The mechanism of this allylation is not fully known, although a cycle involving activation of the aldehyde by the bidentate BINOL-Ti complex followed by the addition of the allyl ligand to the aldehyde, removal of the tributyltin , and transmetallation to regenerate the Ti complex has been proposed. [ 10 ] [ 11 ]
Work performed by Keck and followed up by Faller and coworkers showed a positive nonlinear effect (NLE) correlating the product enantiomeric purity with the BINOL enantiomeric purity. These observations imply that a dimeric meso-chiral catalyst is less active than the homochiral dimers, leading to the observed chiral amplification. [ 10 ] [ 11 ]
Corey and coworkers established a CH-O hydrogen bonding model that accounts for the absolute stereochemistry of the transformation. [ 12 ]
The Tagliavini group, which had carried out asymmetric allylation using a similar BINOL-Ti(IV) complex, followed up early successes by synthesizing a variety of enantiopure substituted binaphthyl ligands. The most successful of these substituted binaphthyls, shown below, gave 92% product enantiomeric excess in the addition of allyltributyltin to aldehydes with a Ti(OiPr)2Cl2 metal complex. [ 13 ]
The Brenna group developed a synthesis for a binol analog, shown below, [ which? ] which can be resolved into its enantiomers quite easily and used as a chiral auxiliary for stereoselective Keck allylations, showing in some cases improved enantiomeric excesses of up to 4% over the (R)-BINOL catalyzed allylations. [ 14 ] Additionally, the developed auxiliary also showed an NLE similar to the classic BINOL, allowing enantio-impure quantities to be used.
Faller's group, whose aforementioned work helped elucidate the chiral amplification of the reaction, also developed the use of diisopropyl tartrate in a chiral poisoning strategy. Diisopropyl tartrate, racemic BINOL, Ti(OiPr)4, phenylaldehyde, and allyltributyltin were used to give enantiomeric excesses of up to 91%. [ 11 ]
Yoshida and coworkers developed a synthesis of dendritic binaphthols that serve as homogenous, easily recoverable catalyst systems, and showed that they were amenable to forming homoallylic alcohols using Keck's allylation conditions. [ 15 ]
Maruoka and Kii developed a bidentate Ti(IV) binol ligand for the allylation of aldehydes with the aim of restricting M-O bond rotation between the lewis acid and the aldehyde in order to improve enantiomeric excesses. The bidentate ligand contains two titaniums, binols, and an aromatic diamine connecting moiety, gave enantiomeric excesses of up to 99%. [ 16 ] Improved stereoselectivity is proposed to come from double activation of the carbonyl from the titaniums, a hypothesis supported by C13 NMR and IR spectroscopy studies on 2,6-γ-pyrone substrate. The most convincing evidence that the M-O rotation is restricted comes from NOE NMR studies on trans-4-methoxy-3-buten-2-one. Radiation of methoxyvinyl protons in free enone and in enone complexed with monodentate Ti(IV) show s-cis and s-trans conformations, while radiation of the enone in a bidentate Ti(IV) complex showed predominantly s-trans conformers. In 2003, this group extended the allylation strategy using this bidentate catalyst to ketones. [ 17 ]
Two key steps in the allylation reaction involve breakage of the Sn-C bond in the allyl fragment and formation of the O-Sn bond to facilitate reproduction of the Ti(IV) catalyst. Chan Mo-Yu and coworkers developed an alkylthiosilane accelerator to promote both of these steps, simultaneously increasing the reaction rate and lowering the required catalyst dosages. [ 18 ] Coupling of phenylaldehyde with allyltributyltin afforded 91% yield and 97% enantiomeric excess of homoallylic alcohol using 10 mol% of the BINOL-Ti(IV) catalyst, however addition of the alkylthiosilane and use of only 5 mol% catalyst gave 80% yield and 95% enantiomeric excess of homoallylic alcohol.
Brueckner and Weigand extended the use of this allylation chemistry to beta-substituted stannanes, including those that contain heterocycles, in 1996, exploring a variety of titanium alkoxides, premixing times, and reaction temperatures. [ 19 ] The optimal discovered conditions were 10 mol% Ti(OiPr)4 or Ti(OEt)4, 20 mol% enantiopure BINOL, with a premixing period of 2 hours, giving enantiomeric excesses of up to 99%. | https://en.wikipedia.org/wiki/Keck_asymmetric_allylation |
KeeLoq is a proprietary hardware-dedicated block cipher that uses a non-linear feedback shift register (NLFSR). The uni-directional command transfer protocol was designed by Frederick Bruwer of Nanoteq (Pty) Ltd., the cryptographic algorithm was created by Gideon Kuhn at the University of Pretoria , and the silicon implementation was by Willem Smit at Nanoteq (Pty) Ltd ( South Africa ) in the mid-1980s. KeeLoq was sold to Microchip Technology Inc in 1995 for $10 million. [ 1 ] It is used in ' hopping code ' encoders and decoders such as NTQ105/106/115/125D/129D, HCS101/2XX/3XX/4XX/5XX and MCS31X2. KeeLoq has been used in many remote keyless entry systems by such companies like Chrysler , [ 2 ] Daewoo , Fiat , Ford , [ 3 ] GM , Honda , Mercedes-Benz , [ 3 ] Toyota , Volvo , Volkswagen Group , Clifford, Shurlok, and Jaguar . [ 3 ]
KeeLoq "code hopping" encoders encrypt a 0-filled 32-bit block with KeeLoq cipher to produce a 32-bit " hopping code ". A 32-bit initialization vector is linearly added ( XORed ) to the 32 least significant bits of the key prior to encryption and after decryption .
KeeLoq cipher accepts 64-bit keys and encrypts 32-bit blocks by executing its single-bit NLFSR for 528 rounds. The NLFSR feedback function is 0x3A5C742E or
KeeLoq uses bits 1, 9, 20, 26 and 31 of the NLFSR state as its inputs during encryption and bits 0, 8, 19, 25 and 30 during decryption. Its output is linearly combined (XORed) with two of the bits of the NLFSR state (bits 0 and 16 on encryption and bits 31 and 15 on decryption) and with a key bit (bit 0 of the key state on encryption and bit 15 of the key state on decryption) and is fed back into the NLFSR state on every round.
This article describes the Classic KeeLoq protocol, but newer versions has been developed. The Ultimate KeeLoq system [ 4 ] is a timer-based algorithm enhancing the Classic KeeLoq system. The goal of this newer version is to contain stronger, industry standard AES-128 cipher which replaces KeeLoq cipher algorithm, and have a timer-driven counter which continuously increments, which is the opposite of the Classic KeeLoq where the counter increments based on the button press. This provides protection against brute-force attack and capture and replay attack , known as RollJam for Samy Kamkar's work.
For simplicity, individual "code hopping" implementations typically do not use cryptographic nonces or timestamping . This makes the protocol inherently vulnerable to replay attacks : For example, by jamming the channel while intercepting the code, a thief can obtain a code that may still be usable at a later stage. [ 5 ] This sort of "code grabber," [ 6 ] while theoretically interesting, does not appear to be widely used by car thieves. [ 7 ]
A detailed description of an inexpensive prototype device designed and built by Samy Kamkar to exploit this technique appeared in 2015. The device about the size of a wallet could be concealed on or near a locked vehicle to capture a single keyless entry code to be used at a later time to unlock the vehicle. The device transmits a jamming signal to block the vehicle's reception of rolling code signals from the owner's fob, while recording these signals from both of his two attempts needed to unlock the vehicle. The recorded first code is forwarded to the vehicle only when the owner makes the second attempt, while the recorded second code is retained for future use. [ 8 ] A demonstration was announced for DEF CON 23. [ 9 ]
KeeLoq was first cryptanalyzed by Andrey Bogdanov using sliding techniques and efficient linear approximations . Nicolas Courtois attacked KeeLoq using sliding and algebraic methods. The attacks by Bogdanov and Courtois do not pose any threat to the actual implementations that seem to be much more vulnerable to simple brute-force of the key space that is reduced in all the code-hopping implementations of the cipher known to date. Some KeeLoq "code grabbers" use FPGA -based devices to break KeeLoq-based keys by brute force within about two weeks due to the reduced key length in the real world implementations. [ citation needed ]
In 2007, researchers in the COSIC group at the university at Leuven , Belgium , (K.U.Leuven) in cooperation with colleagues from Israel found a new attack against the system. [ 10 ] Using the details of the algorithm that were leaked in 2006, the researchers started to analyze the weaknesses. After determining the part of the key common to cars of a specific model, the unique bits of the key can be cracked with only sniffed communication between the key and the car.
Microchip introduced in 1996 [ 11 ] a version of KeeLoq ICs which use a 60-bit seed. If a 60-bit seed is being used, an attacker would require approximately 1011 days of processing on a dedicated parallel brute force attacking machine before the system is broken. [ 12 ]
In March 2008, researchers from the Chair for Embedded Security of Ruhr University Bochum , Germany, presented a complete break of remote keyless entry systems based on the KeeLoq RFID technology. [ 13 ] [ 14 ] Their attack works on all known car and building access control systems that rely on the KeeLoq cipher.
The attack by the Bochum team allows recovering the secret cryptographic keys embedded in both the receiver and the remote control. It is based on measuring the electric power consumption of a device during an encryption. Applying what is called side-channel analysis methods to the power traces, the researchers can extract the manufacturer key from the receivers, which can be regarded as a master key for generating valid keys for the remote controls of one particular manufacturer. Unlike the cryptanalytic attack described above which requires about 65536 chosen plaintext-ciphertext pairs and days of calculation on a PC to recover the key, the side-channel attack can also be applied to the so-called KeeLoq Code Hopping mode of operation (a.k.a. rolling code ) that is widely used for keyless entry systems (cars, garages, buildings, etc.).
The most devastating practical consequence of the side-channel analysis is an attack in which an attacker, having previously learned the system's master key, can clone any legitimate encoder by intercepting only two messages from this encoder from a distance of up to 100 metres (330 ft). Another attack allows one to reset the internal counter of the receiver (garage door, car door, etc.), which makes it impossible for a legitimate user to open the door. [ 15 ] | https://en.wikipedia.org/wiki/KeeLoq |
A Key Klamp is a structural pipe fitting commonly used in the construction of handrails and barriers. Fabricated installations comprise the fittings and separate tubing components, which can be sized on site.
The system was devised in 1934 and is made by a subsidiary of KIG Holdings. The fittings are mostly supplied to third parties for sale to fabricators, with a small proportion of sales being made internally to specialist divisions of the company.
The system was developed in 1934 by George H. Gascoigne and his colleagues in Reading , England for making cows' milking stalls . It was advertised to industrial chemists in 1944, and used for storage systems in factories in the 1960s. By 1980 it was available in Canada, as noted by the Canadian Institute of Mining and Metallurgy
The system comprises unthreaded cast iron or aluminium [ 1 ] [ 2 ] structural tubing and slip-on structural pipe fittings . The galvanized malleable [ 3 ] fittings provide resistance to corrosion and are secured to the tubes using set screws [ 3 ] by use of a hex key . [ 4 ]
Some cutting or bending of the tubes may be required while installing the system, according to site-specific circumstances. Skilled labourers such as welders are not required, but the material costs are higher for the Key Klamp system. [ 5 ] A contractor at the Long Island Rail Road described the system in 2007 as being "very simple to install". [ 4 ]
Also cow stalls, bank operated yard yokes, calf penning, bull corner yokes and bull pen railing.
Example uses of various derived systems are in guard rails [ 1 ] and market stalls. [ 7 ] More unusual uses have been seen in home shelving, [ 8 ] [ 9 ] kite buggying [ 10 ] and the Rover chair . Parkour and Ninja Warrior training facilities have also benefited from the reliable and quick to set up Structural Pipe Fittings. [ 11 ]
In 2003, the company and a former competitor stated that such fittings were not being used in some countries in Europe, in favour of welding. This was due to lower labour costs. For uncomplicated installations, welding may be a cheaper solution than Key Klamp, depending upon usage. [ 5 ]
In 2003, the system dominated the UK and EU markets, with a share of 70–80 per cent . (The fittings market was worth £5–8 million in the UK in 2003.) The premium branding the product is said to hold is due to KIG offering incremental services . [ 5 ] Some customers inherently prefer using such fittings, while others prefer welding. [ 5 ] The choice of system is often made during initial design of an installation. [ 5 ]
The system is marketed for specific uses under various names, including a low-cost brand called Tubeclamp. Specialist divisions of the company exist which fabricate finished structures, although such internal sales of the fittings constitute only a fraction of total fittings sales. [ 5 ]
Between 1998 and 2003, volumes of Key Klamp sales increased. The value of total annual sales remained static throughout this period, associated with an overall price reduction of 20–30 per cent . During this period, the price reduction of a complete system including the tube components was 5–10 per cent . [ 5 ]
A business acquisition by KIG of no frills competitor FastMat (a subsidiary of Access Technologies ) in 2003 led to a report being filed with the UK's Secretary of State for Trade and Industry under the Fair Trading Act 1973 . The report concluded that the merger should not be referred to the Competition Commission due to the relatively inexpensive cost of entry to the market by others. Most suppliers of competing products to the UK import their fittings from low-cost Far East contract manufacturers. [ 5 ] | https://en.wikipedia.org/wiki/Kee_Klamp |
Keen as Mustard is a documentary film researched and directed by Bridget Goodwin detailing secret experiments conducted during World War II on Australian servicemen volunteers to investigate the effects of, and precautions against, mustard gas when used as a weapon in the tropics. The film, released by Film Australia in 1989, contains extensive historic documentary footage and accounts by several participants, and was made possible by the overseas acquisition of documents that remained restricted by the Australian government. A book of the same name was published in 1998, containing much additional material due to the release of some formerly restricted documents by the AWM in 1992. [ 1 ]
In the later days of World War II evidence was found in Papua New Guinea of Japan's preparedness to use chemical weapons , in the form of bombs loaded with a mixture of mustard gas and lewisite . British and American military planners became acutely aware of their lack of knowledge about the effects of such materials on soldiers in tropical areas. An Australian Chemical Warfare Research & Experimental Section was formed in 1942 and a top-secret facility established in Queensland near Innisfail , and later at Gunyarra near Proserpine , [ 2 ] where a wide range of tests was performed by British , American and Australian researchers on volunteers from Australian defence personnel, with nurses and laboratory assistants recruited from the Australian Army Medical Women's Service . Initial tests proved that mustard gas was around four times as potent in tropical climates, with greatest aggravation to the skin occurring in the sweaty areas of the groin, buttocks, back of legs, neck and armpits. Jack Legge & Olive Lucas checking goats in weapons pit prior to mustard gas experiment Brook Island 3 March 1944.jpg
A large 100 cubic metres (3,500 cu ft) controlled environment stainless-steel gas chamber was designed by biochemists J. W. Legge and (later Professor Sir) Hugh Ennor to house volunteer subjects to ascertain the effectiveness of various materials and designs of protective clothing, during periods of physical exertion and after being subject to normal wear and tear. Other tests were conducted to determine the limits of endurance of soldiers in performing arduous tasks after bodily exposure to mustard gas. Gas masks or respirators were used to minimise inhalation of the gas.
The determined resistance put up by Japanese soldiers against the Americans in their assault on Tarawa in November 1943 prompted the US Army, which had sustained terrible losses in taking the island, to make plans for use of chemical weapons in further attacks of the kind. General Douglas MacArthur was in favor of this approach, heavy naval bombardment having been unexpectedly ineffective at lowering the enemy's resistance. North Brook Island , off the Queensland coast around 30 km east of Cardwell , was prepared with various forms of tunnel and foxhole to simulate the kind of emplacements used by the Japanese army, and goats tethered in these locations. Bombers then carpeted the island with mustard gas bombs and the following day unprotected Australian soldiers were landed on the island to assess the damage, and spent 12 hours there, suffering some lung damage and blisters where their bodies came into contact with contaminated foliage.
The Allies never used gas against the enemy, as Japan surrendered following the dropping of atom bombs on Hiroshima and Nagasaki. The Chemical Warfare Unit was top secret and its very existence was denied for many years. Many of the volunteers had never served overseas, and so did not receive the monitoring and preferential health treatment accorded other ex-servicemen by the Department of Veterans' Affairs . Mustard gas is known to damage DNA by alkylation , and it has been suggested that the experiments were responsible for adverse long-term health effects on some of these volunteers. [ citation needed ]
The film was in 1989 Highly Commended in the Walkley Awards for Australian Journalism. [ 3 ]
Bridget Goodwin was a journalist working for the Australian Broadcasting Corporation before turning her hand to documentary film making. She has also produced documentary films about the author Hugh Lunn , the Henry Lawson Festival in Grenfell , New South Wales and Professor Manning Clark . [ 4 ]
The Brook Island trials were much more extensive than this documentary film suggests, relying largely on the evidence of a few participants. There were at least three major trials on the island, listed here . This article also mentions unsubstantiated stories about the use of human guinea-pig volunteers from American prisons.
The Australian War Memorial , Canberra has a great deal of material, freely available, related to the Australian Chemical Warfare Research & Experimental Section, some of which is reproduced here .
Goodwin wrote an essay on her research and the making of the film for the series "Working with Knowledge" conference papers online, Session 6 entitled "Science Archives: Humanising and Popularising the Stories", available here | https://en.wikipedia.org/wiki/Keen_as_Mustard_(film) |
Keepers are substances (typically solvents , but sometimes adsorbent solids) added in relatively small quantities during an evaporative procedure in analytical chemistry, such as concentration of an analyte-solvent mixture by rotary evaporation . The purpose of a keeper is to reduce losses of a target analyte during the procedure. Keepers typically have reduced volatility and are added to a more volatile solvent.
In the case of volatile target analytes, it is difficult to totally avoid loss of the analyte in an evaporative procedure, but the presence of a keeper solvent or solid is intended to preferentially solvate or adsorb the analyte, so that the volatility of the analyte is reduced as the evaporative procedure continues. In the case of non-volatile target analytes, the presence of the keeper solvent or solid is intended to prevent all the solvent from being evaporated off, thereby preventing the loss of analytes which might irreversibly adsorb to the container walls when completely dried, or if it is totally dried (in the case of a solid keeper), provide a surface where the analyte can be reversibly rather than irreversibly adsorbed. [ 1 ] A solid keeper of sodium sulfate has been shown to be effective for reducing losses of polycyclic aromatic hydrocarbons (PAHs) in evaporative procedures. [ 2 ]
The following solvents are commonly used as keepers: [ 1 ]
This article about analytical chemistry is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Keeper_(chemistry) |
The Keetch–Byram drought index ( known as KBDI ), created by John Keetch and George Byram in 1968 for the United States Department of Agriculture 's Forest Service , is a measure of drought conditions. It is commonly used for the purpose of predicting the likelihood and severity of wildfires . It is calculated based on rainfall, air temperature, and other meteorological factors. [ 1 ]
The KBDI is an estimate of the soil moisture deficit, which is the amount of water necessary to bring the soil moisture to its full capacity. A high soil moisture deficit means there is little water available for evaporation or plant transpiration . [ 2 ] This occurs in conditions of extended drought , and has significant effects on fire behaviour.
In the United States, it is expressed as a range from 0 to 800, referring to hundredths of an inch of deficit in water availability; in countries that use the metric system , it is expressed from 0 to 200, referring to millimetres. [ 3 ]
This article about atmospheric science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Keetch–Byram_drought_index |
The Keggin structure is the best known structural form for heteropoly acids . It is the structural form of α-Keggin anions, having a general formula of [XM 12 O 40 ] n − , where X is the heteroatom (most commonly are pentavalent phosphorus P V , tetravalent silicon Si IV , or trivalent boron B III ), M is the addendum atom (most common are molybdenum Mo and tungsten W), and O represents oxygen . [ 1 ] The structure self-assembles in acidic aqueous solution and is a commonly used as a type of polyoxometalate catalysts .
The first α-Keggin anion, ammonium phosphomolybdate ( [NH 4 ] 3 [PMo 12 O 40 ] ), was first reported by Jöns Jakob Berzelius in 1826. In 1892, Blomstrand proposed the structure of phosphomolybdic acid and other poly-acids as a chain or ring configuration. Alfred Werner , using the coordination compounds ideas of Copaux, attempted to explain the structure of silicotungstic acid . He assumed a central group, [SiO 4 ] 4− ion, enclosed by four [RW 2 O 6 ] + , where R is a unipositive ion. The [RW 2 O 6 ] + are linked to the central group by primary valences. Two more R 2 W 2 O 7 groups were linked to the central group by secondary valences. This proposal accounted for the characteristics of most poly-acids, but not all. [ citation needed ]
In 1928, Linus Pauling proposed a structure for α-Keggin anions consisting of a tetrahedral central ion, [XO 4 ] n −8 , caged by twelve WO 6 octahedra. In this proposed structure, three of the oxygen on each of the octahedra shared electrons with three neighboring octahedra. As a result, 18 oxygen atoms were used as bridging atoms between the metal atoms. The remaining oxygen atoms were bonded to a proton . This structure explained many characteristics that were observed such as basicities of alkali metal salts and the hydrated form of some of the salts. However the structure could not explain the structure of dehydrated acids. [ citation needed ]
James Fargher Keggin with the use of X-ray diffraction experimentally determined the structure of α-Keggin anions in 1934. The Keggin structure accounts for both the hydrated and dehydrated α-Keggin anions without the need for significant structural change. The Keggin structure is the widely accepted structure for the α-Keggin anions. [ 2 ]
= +
The structure has full tetrahedral symmetry and is composed of one heteroatom surrounded by four oxygen atoms to form a tetrahedron . The heteroatom is located centrally and caged by 12 octahedral MO 6 units linked to one another by the neighboring oxygen atoms. There are a total of 24 bridging oxygen atoms that link the 12 addenda atoms. The metal centres in the 12 octahedra are arranged on a sphere almost equidistant from each other, in four M 3 O 13 units, giving the complete structure an overall tetrahedral symmetry. The bond length between atoms varies depending on the heteroatom (X) and the addenda atoms (M). For the 12–phosphotungstic acid, Keggin determined the bond length between the heteroatom and each the four central oxygen atoms to be 1.5 Å . The bond length forms the central oxygen to the addenda atoms is 2.43 Å. The bond length between the addenda atoms and each of the bridging oxygen is 1.9 Å. The remaining 12 oxygen atoms that are each double bonded to an addenda atom have a bond length of 1.70 Å. The octahedra are therefore distorted. [ 3 ] [ 4 ] This structure allows the molecule to hydrate and dehydrate without significant structural changes and the molecule is thermally stable in the solid state for use in vapor phase reactions at high temperatures (400−500 °C). [ 5 ]
Including the original Keggin structure there are 5 isomers , designated by the prefixes α-, β-, γ-, δ- and ε-. The original Keggin structure is designated α. These isomers are sometimes termed Baker, Baker–Figgis or rotational isomers, [ 6 ] These involve different rotational orientations of the Mo 3 O 13 units, which lowers the symmetry of the overall structure.
The term lacunary is applied to ions which have a fragment missing, sometimes called defect structures. Examples are the [XM 11 O 39 ] n − and [XM 9 O 34 ] n − formed by the removal from the Keggin structure of sufficient Mo and O atoms to eliminate 1 or 3 adjacent MO 6 octahedra. The Dawson structure is made up of two Keggin lacunary fragments with 3 missing octahedra.
The cluster cation [Al 13 O 4 (OH) 24 (H 2 O) 12 ] 7+ has the Keggin structure with a tetrahedral Al atom in the centre of the cluster coordinated to 4 oxygen atoms. The formula can be expressed as [AlO 4 Al 12 (OH) 24 (H 2 O) 12 ] 7+ . [ 7 ] This ion is generally called the Al 13 ion. A Ga 13 analogue is known [ 8 ] an unusual ionic compound with an Al 13 cation and a Keggin polyoxoanion has been characterised. [ 9 ]
Due to the similar aqueous chemistries of aluminium and iron, it was earlier thought that an analogous iron polycation should be isolatable from water. Moreover, in 2007, the structure of ferrihydrite was determined and shown to be built of iron Keggin ions. [ 10 ] This further captured scientists' imagination and drive to isolate the iron Keggin ion. In 2015, the iron Keggin ion was isolated from water, but as a polyanion with a −17 charge; and protecting chemistry was required. [ 11 ] Iron-bound water is very acidic; so it is difficult to capture the intermediate Keggin ion form without bulky and nonprotic ligands instead of the water that is found in the aluminum Keggin ion. However, more important in this synthesis was the bismuth ( Bi 3+ ) counterions that provided high positive charge to stabilize the high negative charge of the heptadecavalent polyanion. [ citation needed ]
The stability of the Keggin structure allows the metals in the anion to be readily reduced . Depending on the solvent , acidity of the solution and the charge on the α-Keggin anion, it can be reversibly reduced in one- or multiple-electron steps. [ 12 ] For example, the silicotungstate anion can be reduced a −20 state. [ 13 ] Some anions such as silicotungstic acid are strong enough as an acid as sulfuric acid and can be used in its place as an acid catalyst. [ citation needed ]
In general α-Keggin anions are synthesized in acidic solutions. For example, 12- phosphotungstic acid is formed by condensing phosphate ion with tungstate ions. The heteropolyacid that is formed has the Keggin structure. [ 5 ]
α-Keggin anions have been used as catalyst in the following reactions: hydration , polymerization and oxidation reaction as catalysts. [ 5 ] Japanese chemical companies have commercialized the use of the compounds in hydration of propene , oxidation of methacrolein , hydration of isobutene and n -butene , and polymerization of THF . [ 14 ] [ 15 ]
12- Phosphotungstic acid , the compound James F. Keggin used to determine the structure, can be purchased commercially. Other compounds that contain the α-Keggin anion such as silicotungstic acid and phosphomolybdic acid are also commercially available at Aldrich Chemicals , Fisher Chemicals, Alfa Aesar , VWR Chemical, American Elements , and others. [ citation needed ] | https://en.wikipedia.org/wiki/Keggin_structure |
Keiichi Itakura ( 板倉 啓壹 , Itakura Keiichi , born February 18, 1942 in Tokyo , Japan) is an organic chemist and a Professor in the Department of Molecular and Cellular Biology at the Beckman Research Institute at City of Hope National Medical Center . [ 1 ] [ 2 ]
Itakura was born in Tokyo , Japan on February 18, 1942. He obtained a PhD in Organic Chemistry at Tokyo Pharmaceutical College in 1970. He then accepted a fellowship with Saran A. Narang at the Division of Biological Sciences, National Research Council of Canada , to work on DNA synthesis . [ 2 ]
In 1975, Itakura joined the City of Hope National Medical Center. There he was part of a team of scientists including Arthur Riggs who developed recombinant DNA technology. By 1976, the first artificial gene had been synthesized, by Har Gobind Khorana at MIT , and the possibility of synthesizing insulin through bacterial fermentation by incorporating a gene for insulin into a bacterium such as E. coli had been suggested. [ 3 ] [ 4 ]
Itakura and others succeeded in synthesizing a plasmid containing chemically synthesized lac operator in 1976, using a technique they called "linker technology". [ 5 ]
"We used the technology that Itakura was the master of to make small pieces of DNA, which greatly improved the ability to cut and splice exactly where you wanted. We devised how you can put them exactly where you want them... That was a major contribution." Arthur Riggs [ 6 ]
In 1977, Itakura successfully synthesized the gene for somatostatin . [ 7 ] [ 8 ] Production of somatostatin, a hormone produced in the human brain, was not expected to be commercially significant. However, the work was considered a possible first step towards the creation of a synthetic insulin. Building on Khorana's work, Itakura developed a technique that reduced the time involved in successful synthesis from years to weeks. [ 4 ] He then inserted the gene for somatostatin into E. coli . [ 8 ] This was the first demonstration of a foreign gene inserted into E. coli. [ 2 ] [ 7 ] [ 9 ] [ 10 ]
By 1978 Herbert Boyer 's biotechnology startup Genentech had contracted with Riggs and Itakura, [ 4 ] and Boyer and Itakura had created a plasmid coded for human insulin . Genentech signed a joint-venture agreement with Eli Lilly and Company to develop and market the technology. Their product, Humulin, approved in 1982 by the FDA, was the first biotechnology product to be marketed. [ 7 ] Genentech patented techniques that list Itakura and Riggs as the inventors, and are known as the Riggs-Itakura patents. [ 11 ] [ 12 ] As their principal organic chemist, Keiichi Itakura was essential to the success of Genentech's development of synthetic insulin. [ 4 ] [ 13 ] His work on recombinant DNA technology has had a significant impact in molecular biology and biochemistry. [ 2 ] [ 4 ]
Keiichi Itakura became a senior research scientist at City of Hope in 1980. [ 2 ] In 1982, he formed the Department of Molecular Genetics (later the Department of Molecular and Cellular Biology). [ 14 ] Itakura became director of City of Hope's genetics laboratory in 1989. [ 2 ] As of 2016 [update] he continues to work and teach at City of Hope. [ 1 ] | https://en.wikipedia.org/wiki/Keiichi_Itakura |
Keiji Morokuma (諸熊 奎治, Morokuma Keiji ; July 12, 1934 – November 27, 2017) was a Japanese theoretical chemist and chemical engineer known for developing energy decomposition analysis for molecular interactions [ 1 ] and the ONIOM method in quantum chemistry . [ 2 ] [ 3 ] [ 4 ]
Morokuma was born in Kagoshima , Kagoshima Prefecture and studied engineering at Kyoto University . As a student of the Nobel laureate Kenichi Fukui , one of the pioneers of quantum chemistry in Japan, at Kyoto University , Morokuma received his doctorate in 1963 in fuel chemistry. [ 5 ] He became research associate at Kyoto University until 1966, when he became a postdoc at Harvard University with Martin Karplus working on reaction dynamics as a Fulbright visiting scholar. [ 6 ] Afterwards, he joined the Department of Chemistry at the University of Rochester as an assistant professor in 1967 and eventually became a full professor in 1971. He stayed at Rochester until 1976 before moving to the Institute for Molecular Science in Okazaki, Japan and worked there until 1993. From 1978 to 1993, Morokuma was also the director of the Computer Center at the institute. In 1993, Morokuma moved back to the US and became the William Henry Emerson Professor of Chemistry at Emory University . He retired from Emory University in 2006 and traveled back to Japan, where he became a senior research fellow at the Fukui Institute for Fundamental Chemistry in Kyoto University . He remained in Kyoto until his death in 2017. [ 3 ]
Morokuma developed the ONIOM method, [ 7 ] a method that integrates molecular orbit methods and those of molecular mechanics at several levels and uses them to calculate large molecules. [ 8 ] He investigated potential surfaces in chemical reactions and reactions and structure of nanoparticles, proteins and transition metal complexes as well as photochemistry of excited state molecules and biomolecules. [ 2 ] [ 9 ] [ 4 ]
Morokuma was a Sloan Research Fellow in 1970. In 1978, he received the Prize of the International Academy of Quantum Molecular Science , of which he was a member. In 1991, he was the first to receive the Schrödinger Medal . In 1992 the Prize of the Japanese Chemical Society, in 2005 the Fukui Medal of the Asian Pacific Association of Theoretical & Computational Chemists and in 2008 the Imperial Prize of the Japan Academy . In 2009, he was recognized as the Person of Cultural Merit in Japan. [ 3 ] [ 10 ] | https://en.wikipedia.org/wiki/Keiji_Morokuma |
Keiko Hattori is a geochemist and mineralogist . She is Distinguished University Professor of Geochemistry and Mineral Deposits in the Department of Earth and Environmental Sciences at the University of Ottawa . [ 1 ]
Hattori is most known for her research on aspects of Earth's atmospheric and mantle evolution, as well as the formation of arc volcanoes and the generation of metal-fertile volcanic arcs. Her application of this knowledge has led to insights regarding the origins and locations of mineral deposits. Specifically, she has conducted research on the transfer of chalcophile elements ( copper -like elements) from slabs to arc magmas through mantle wedges , as well as from arc magmas to mineral deposits. Additionally, her work has encompassed exploration geochemistry, where she has investigated the dispersion of metals from buried deposits including platinum and palladium in surface media. She was appointed as the 2022 International Exchange Lecturer of the Society of Economic Geologists (SEG), [ 2 ] and has been the recipient of the Island Arc Award and the Takeo Kato Gold Medal. [ 3 ]
Hattori is an elected Fellow of the Royal Society of Canada [ 4 ] and Mineralogical Society of America . [ 5 ]
Hattori was the first female undergraduate student in the Geology Department at the University of Tokyo , which was established in 1877. She completed her master's and PhD in isotope geochemistry there. [ 6 ]
Hattori began her academic career as a postdoctoral researcher at the University of Alberta in Edmonton in 1977 and participated in the International Drilling project as a Canadian delegate to study volcanic rocks and thermal alteration in Iceland. [ 7 ] In 1980, she moved to the University of Calgary as a research associate jointly affiliated with the Department of Physics and the Department of Geology and Geophysics. Three years later, she joined the University of Ottawa as an assistant professor and was promoted to associate professor in the Department of Geology in 1987. [ 6 ]
She was the first female professor in earth science departments within the national capital region as well as the first female professor of mineral deposits in Canada. In 1994 she became full professor in the Department of Earth and Environmental Sciences at the University of Ottawa. [ 8 ] She was awarded the title of Distinguished University Professor in 2023 for her contributions to scientific research and education. [ 9 ]
Hattori has held numerous administrative appointments throughout her career. From July 1991 to June 1994, she served as the director of the Ottawa-Carleton Geoscience Centre. [ 10 ] In 2004, she was appointed as the department chair for Earth Sciences at the University of Ottawa, a position she held for four years. [ 11 ]
Apart from the administrative work related to universities, she has been engaged in the activities of several scientific organizations including Mineralogical Society of America, [ 12 ] Society of Economic Geologists, [ 13 ] and Royal Society of Canada. She is Director of Earth, Ocean and Atmosphere Science Division of Royal Society of Canada (2021-2024). [ 14 ]
Hattori was an appraiser of graduate-research programs at various Ontario Universities (1999-2002) and geoscience program reviewers of American University of Beirut in Lebanon (2016-17), Western University (2012) and Hiroshima University (2009). [ 1 ]
Hattori has been appointed as visiting professor at Université de Lyon (1999) and l’ Universiteé Grenoble (2016), visiting scientist at Japan Marine Science and Technology (2003-2004), visiting professor at Nagoya Institute , [ 15 ] Guest Research Scientists at Woods Hole Oceanographic Institution (1995-1996), Visiting Research Scientist at Massachusetts Institute of Technology (1989-1990). [ 1 ] [ 16 ]
Hattori has made contributions to the field of earth sciences , utilizing trace element geochemistry and stable and radiogenic isotopes to understand the earth processes. During the early stages of her career, she focused on studying active volcanoes and associated hydrothermal activity. However, a tragic accident atop a Colombian volcano, resulting in the loss of several colleagues, prompted her to shift her research focus to ancient volcanic terranes in Canada. Over the past 14 years, she has conducted research in various regions of subduction zones worldwide, where oceanic crust subducts and forms arc volcanoes and mountain belts. Her investigations involve examining rocks and collecting samples to analyze the intricate processes of subduction and the subsequent return of materials to the surface through volcanoes. Her research areas have included the Himalayas ( Northern Pakistan , Northern India ), Italian and French Alps , Turkey , China , Japan , Philippines , Peru , and the Dominican Republic . [ 6 ]
Hattori's contributions to the earth sciences primarily center on utilizing the abundance of redox-sensitive elements and their isotopic compositions to interpret processes from the surface to the mantle. Her discoveries include the timing of the abrupt rise in atmospheric oxygen content at around 2.2 billion years ago during Earth's evolution, the definition of osmium isotope evolution in the mantle, the identification of serpentine as the reservoir of water and fluid-mobile elements in the mantle, and the provision of evidence that oxidized mafic magmas bring base metals and sulfur from the mantle to form giant copper deposits that supply many critical metals for society. In addition, her work has contributed to the discovery of such critical metal deposits through the mobility of metals in surface waters . [ 17 ]
Hattori presented evidence in her Nature paper that, resolved the long-standing debate regarding the timing of the change in ancient Earth's surface oxidation. Her findings demonstrated that atmospheric oxygen levels were still low around 2.4 billion years ago, during the early Proterozoic, based on detailed sulfur isotope analysis of sedimentary rocks on the north shore of Lake Huron. [ 18 ] In her subsequent work published in Science , she revealed that atmospheric oxygen levels sharply rose within the sedimentary sequence at about 2.3 billion years. [ 19 ]
Hattori also highlighted the role of volcanic processes in shaping the surface redox condition, challenging the previously held belief that increased photosynthesis was solely responsible for the oxidation of Earth's surface environment. [ 20 ] Subsequent work provided further confirmation of the crystallization of oxidized magmatic sulfates during igneous crystallization, [ 21 ] as well as the presence of such sulfate minerals in ancient (2.6 billion years old) igneous rocks. [ 22 ]
Hattori defined the osmium isotope evolution of Earth's mantle, providing evidence for an accretion of chondritic meteorites after the core-mantle separation. [ 23 ]
Prior to Hattori's research, the origin of large nuggets of platinum-group metals in streams was a subject of debate, with some proposing river water formation under a tropical climate and others suggesting mechanical erosion from rocks. However, her research presented evidence supporting their formation in rocks at high temperatures, followed by erosion to streams. [ 24 ] [ 25 ] [ 26 ]
Through Hattori's research, it was also revealed that platinum grains found in streams contain oxygen, which led to initial suggestions of platinum oxide; however, using synchrotron techniques, it was demonstrated that the oxygen is combined with iron, not with platinum. [ 27 ]
Hattori argued that the prevailing view for volcano formation in arcs ic arc formation, that water is released rapidly from subducting slabs when they are metamorphosed to eclogite facies, is inconsistent with geological evidence. Instead, she proposed an alternative mechanism, suggesting that water is continuously released from slabs and stored as serpentinites (hydrated mantle rocks) and stressed that the subsequent dehydration of these serpentinites triggers the formation of arc volcanoes. Her work has established the importance and distribution of serpentinites on the major ocean floors, which control seismic activity and may potentially have played a role in the origin of life on the planet. [ 28 ] [ 29 ] [ 30 ]
Additionally, Hattori's work highlighted that heavy metals and metalloids, such as arsenic and antimony, are generally considered to be concentrated in sulphides, but under sulphur-deficient conditions, these elements behave like normal rock-forming elements. [ 30 ] [ 31 ]
Hattori and De Hoog, after considering the debate surrounding the cause of varying oxidation conditions in igneous rocks at shallow crustal levels, documented that highly oxidized conditions of rocks are an intrinsic character of the source magma in the mantle. [ 32 ] They emphasized the capability of oxidized magmas to transport large quantities of sulfur and metals as well.
In her 1995 work, Hattori provided the initial documentation of oxidized arsenic in the overall reduced mantle, as arsenic is present by replacing Si. One of her PhD students, Jian Wangm, evaluated the redox state of mantle rocks and discovered that carbon is the primary control for the oxidation conditions of the mantle in subduction zones. [ 33 ]
Hattori's research interest has also extended to porphyry-type deposits, which supply critical metals such as copper, molybdenum, and gold. Through her research, she presented evidence supporting the notion that sulfur and metals have their origin in the mantle, [ 34 ] [ 35 ] and proposed that they were extracted and transported by mafic magmas from the mantle to shallow crustal levels. This proposal was based on her earlier work on Pinatubo eruption products, where metals and sulphur are released from mafic magmas during their ascent and incorporated into overlying erupted felsic magmas. [ 21 ] Furthermore, Cees-Jan DeHoog, her postdoctoral research fellow, provided evidence that oxidized magmas are capable to transport metals and sulphur from deep in the mantle to shallow levels of crust. [ 32 ]
Hattori developed analytical methods that demonstrated the high mobility of palladium as soluble neutral to anionic complexes in surface waters. This behavior allows the metal to disperse widely from its sources, and to become incorporated into plants and organic-rich soil. [ 36 ] Her research findings have been presented at various industry-oriented workshops, including short courses associated with the International Platinum Conference in Oulu, Finland, and the Prospectors and Developers Association meeting in Toronto. In addition, her research provided a contrasting perspective to the previously assumed origin of metals in peat from the Hudson Bay Lowland. While it was previously assumed that the metals in peat originated from industrial activity far south of the northern region, she demonstrated that the compositions of ombrotrophic peat are strongly influenced by the underlying rocks, even those located as deep as 20 metres below the surface. This observation further highlighted that the composition of peat may serve as a useful indicator to locate concealed deposits, including kimberlites, which are host to diamonds. [ 37 ]
Hattori also examined sturdy minerals that can be dispersed by streams and glaciers to evaluate their usefulness in finding mineral deposits. | https://en.wikipedia.org/wiki/Keiko_Hattori |
Keith A. Buzzell (1932–2018) was an American osteopathic physician, lecturer, author, and practitioner of the Gurdjieff Work , also known as the Fourth Way . His work focused on bridging the teachings of G.I. Gurdjieff with contemporary understandings of science, consciousness, neurophysiology, and education.
Buzzell was born in 1932 and developed an early interest in music, philosophy, science and mysticism. In 1950, at the age of eighteen, he purchased G.I. Gurdjieff's All and Everything sparking a lifelong engagement with the Gurdjieff's work. He attended Bowdin College on a full scholarship before transferring to Boston University , where he earned an A.B. in 1955. Initially studying music, he later shifted his focus to medicine, earning a Doctor of Osteopathic Medicine ( D.O. ) degree from the Philadelphia College of Osteopathic Medicine in 1960. During his studies in Philadelphia, he helped establish a free clinic. He completed an internship at the Osteopathic Hospital of Maine in 1961, and took a Fellowship at Kirksville College of Osteopathic Medicine in 1962 where he also taught.
Buzzell established a family practice in Fryeburg, Maine , in 1969 where he served the community until his retirement in 2010. He was also the medical director of Fryeburg Health Care Center from 1982 until 2018. Throughout his career, he played key roles in various health-related organizations, including founding and directing Hospice of Western Maine (1989 to 1995). He also served as adjunct clinical faculty for New England College of Osteopathic Medicine (1987–1997).
His medical publications included “History of Manipulative Therapeutics" (1962), Osteopathic Theory and Methods (1967-1969, in four volumes) and Neurophysiologic Basis of Osteopathic Practice (1969), [ 1 ] and The Children of Cyclops: The Influence of Television Viewing on the Developing Human Brain (1998).
Buzzell was a lifelong student of the Gurdjieff Work. [ 2 ] In 1971, he met Irmis Popoff, [ 3 ] [ 4 ] a student of Gurdjieff and Ouspensky , and worked under her guidance until the mid-1980s. Later, he corresponded with Annie Lou Staveley, founder of the Two Rivers Farm Work community in Oregon, until her passing in 1996.
Buzzell authored multiple books on Gurdjieff's teachings, including Perspectives on Beelzebub’s Tales (2005), Explorations in Active Mentation: Re-Membering Gurdjieff’s Teaching (2006), Man: A Three-brained Being (2007), Reflections on Gurdjieff’s Whim (2012), A New Conception of God (2013), and The Third Striving ( 2014). He also contributed essays to the quarterly journal Stopinder. A Gurdjieff Journal for our Time and presented papers at the All and Everything International Humanities Conference between 1996 and 2012.
Buzzell explored the intersection of Gurdjieff’s philosophy with modern neuroscience, particularly regarding the impact of television on brain development. His 1998 book, The Children of Cyclops: The Influence of Television Viewing on the Developing Human Brain , built upon Paul MacLean's triune brain theory, aligning it with Gurdjieff’s concept of the three-brained being. He argued that modern media conditions human perception and affects neural processing before higher cognitive faculties can assess information critically. Suggestibility was identified by Gurdjieff as one of the chief problems of human psychology. [ 5 ] Buzzell's work highlighted the vulnerability 220 million years of brain and sensory evolution play in conditioning all organisms to accept neural images as necessarily real. Gurdjieff's teaching was considered by Buzzell to be a crucial bridge between science and spirituality. [ 6 ] [ 7 ] [ 8 ] He also sought to cast modern scientific concepts, such as the electromagnetic spectrum of energy, in terms commensurate with Gurdjieff's cosmology. [ 9 ] In addition, Buzzell sought to recast standard scientific terminology and conceptualizations of physical laws (such as the four fundamental forces, chemical bonding, mass-energy equivalence, etc.) into psychological frameworks based on the utilization of attention. [ 10 ] [ 11 ]
Buzzell proposed a novel interpretation of the enneagram, a symbol first introduced by Gurdjieff, [ 12 ] suggesting that the First Series of Gurdjieff’s All and Everything was structured according to an enneagrammatic framework. [ 13 ] He developed a unique derivation of the enneagram he called A Symbol of the Cosmos and Its Laws [ 14 ] and presented his research at the International Humanities Conference s beginning in1996.The video presentation at right gives a holistic view of this synthesis. | https://en.wikipedia.org/wiki/Keith_A._Buzzell |
Keith Henry Stockman Campbell (23 May 1954 – 5 October 2012) [ 1 ] was a British biologist who was a member of the team at Roslin Institute that in 1996 first cloned a mammal, a Finnish Dorset lamb named Dolly , from fully differentiated adult mammary cells. He was Professor of Animal Development at the University of Nottingham . [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] In 2008, he received the Shaw Prize for Medicine and Life Sciences jointly with Ian Wilmut and Shinya Yamanaka for "their works on the cell differentiation in mammals".
Campbell was born in Birmingham , England, to an English mother and Scottish father. He started his education in Perth , Scotland, but, when he was eight years old, his family returned to Birmingham, where he attended King Edward VI Camp Hill School for Boys . [ 8 ] He obtained his Bachelor of Science degree in microbiology from the Queen Elizabeth College , University of London (now part of King's College London ). [ 9 ] In 1983 Campbell was awarded the Marie Curie Research Scholarship, which led to postgraduate studies and later his PhD from the University of Sussex [ 10 ] (Brighton, England, UK). [ 11 ] [ 12 ] [ 13 ]
Campbell's interest in cloning mammals was inspired by work done by Karl Illmensee and John Gurdon . [ citation needed ] Working at the Roslin Institute since 1991, Campbell became involved with the cloning efforts led by Ian Wilmut . In July 1995 Keith Campbell and Bill Ritchie succeeded in producing a pair of lambs, Megan and Morag from embryonic cells, which had differentiated in culture.
In 1996, a team led by Ian Wilmut with Keith Campbell as the main contributor, used the same technique and shocked the world by successfully cloning a sheep from adult mammary cells. Dolly, a Finn Dorset sheep named after the singer Dolly Parton , was born in 1996 and lived to be six years old (dying from a viral infection and not old age, as has been suggested). Campbell had a key role in the creation of Dolly, as he had the crucial idea of co-ordinating the stages of the "cell cycle" of the donor somatic cells and the recipient eggs and using diploid quiescent or "G0" arrested somatic cells as nuclear donors. In 2006, Ian Wilmut admitted that Campbell deserved "66 per cent" of the credit. [ 14 ]
In 1997, Ritchie and Campbell in collaboration with PPL (Pharmaceutical Proteins Limited) created another sheep named "Polly", created from genetically altered skin cells containing a human gene. [ 15 ] In 2000, after joining PPL Ltd, Campbell and his PPL team (based in North America) were successful in producing the world's first piglets by Somatic-cell nuclear transfer (SCNT), the so-called cloning technique. Furthermore, the PPL teams based in Roslin, Scotland and Blacksburg (USA) used the technique to produce the first gene targeted domestic animals as well as a range of animals producing human therapeutic proteins in their milk. [ 16 ] [ 17 ]
From November 1999, Campbell held the post of Professor of Animal Development, Division of Animal Physiology, School of Biosciences at the University of Nottingham where he continued to study embryo growth and differentiation. He supported the use of SCNT for the production of personalised stem cell therapies and for the study of human diseases and the use of cybrid embryo production to overcome the lack of human eggs available for research. Stem cells can be isolated from embryonic, fetal and adult derived material and more recently by overexpression of certain genes for the production of "induced pluripotent cells". Campbell believed all potential stem cell populations should be used for both basic and applied research which may provide basic scientific knowledge and lead to the development of cell therapies. [ 18 ] [ 19 ] [ 20 ] [ 21 ]
In 2008, he received the Shaw Prize for Medicine and Life Sciences jointly with Ian Wilmut and Shinya Yamanaka. [ 22 ] He was awarded the Pioneer Award from the International Embryo Transfer Society posthumously in 2015. [ 23 ]
Campbell died on 5 October 2012, aged 58, after accidentally hanging himself in his bedroom at his Ingleby, Derbyshire home, whilst heavily intoxicated. It was determined at the inquest that he had been behaving erratically at the time and had no actual intention to kill himself; the verdict was a death by misadventure . [ 24 ] [ 25 ] He was buried at Bretby Crematorium, Derbyshire . [ 26 ] He is survived by his wife, Kathy, and two daughters, Claire and Lauren. | https://en.wikipedia.org/wiki/Keith_Campbell_(biologist) |
Keith Fagnou (June 27, 1971 – November 11, 2009) was a Canadian organic chemist and studied education and was a professor of chemistry at University of Saskatchewan and associate professor of organic chemistry at the University of Ottawa . His research focused on developing new reactions that avoid unnecessary activation of substrates and that can instead directly functionalize C–H bonds of simple molecules and introduce C–C bonds. [ 1 ]
Dr. Keith Fagnou was born on June 27, 1971, in Saskatoon , Saskatchewan . Fagnou, a former naval reserve officer, pursued studies at the University of Saskatchewan and received a Bachelor of Education (B.Ed.) in 1995. After teaching at the high school level for a short period, he continued his studies in chemistry at the University of Toronto in 1998 under the supervision of Mark Lautens. In 2000 he received his M.Sc. degree, and in 2002 his Ph.D. Professor Lautens said that Keith "was exceptionally bright and exceptionally down-to-earth and was the most productive person, in the history of his research group." [ 2 ] After his PhD, he joined the faculty at the University of Ottawa as an assistant professor and in 2007 was promoted to associate professor with tenure and awarded a University of Ottawa Research Chair in the Development of Novel Catalytic Transformations. [ 3 ]
While at the University of Ottawa, he established a research program primarily devoted to the development of novel "direct arylation" reactions which allow for the rapid synthesis of important building blocks in medicinal chemistry. [ 4 ] Of note, the development of direct arylation of benzene [ 5 ] and pyridine N-oxide. [ 6 ] Members of his research group are sometimes referred to as "The Fagnou Factory". [ 7 ] His contributions in the field were rewarded with numerous awards and have been included in reviews published on the subject. [ 8 ]
Dr. Keith Fagnou died of complications resulting from a H1N1 influenza infection on November 11, 2009, at the age of 38. [ 9 ]
The University of Ottawa established the "Keith Fagnou Scholarship in Science" in his memory. [ 10 ] The members of his research group also organized a symposium (KFOS) in his honour which was held May 5–7, 2010. [ 11 ] The Pacifichem chemistry conference also held a memorial symposium titled "C-H Functionalization, Memorial Symposium for Professor Keith Fagnou". [ 12 ] In 2011, Keith was recognized as the #77 chemist in the world over the period 2000-2010 on the basis of citations per paper, according to Thomson-Reuters' Sciencewatch.com. [ 13 ] | https://en.wikipedia.org/wiki/Keith_Fagnou |
Keith Christopher Rowley MP (born 24 October 1949) is a Trinidad and Tobago politician who served as the seventh prime minister of Trinidad and Tobago from 2015 to 2025. He was the leader the People's National Movement (PNM) from 2010 to 2025 and was Leader of the Opposition from 2010 to 2015. He also served as the Member of the House of Representatives for Diego Martin West from 1991 to 2025. [ 7 ] He is a volcanologist by profession, holding a doctorate in geology, specializing in geochemistry. [ 8 ]
Rowley was born in Mason Hall, Tobago , [ 9 ] raised by his grandparents, who were prominent Tobago farmers. [ 10 ] He was a pupil of Bishop's High School in Tobago, and graduated from the University of the West Indies (Mona) from where he graduated with a BSc. Geology (First Class Honors). [ 11 ] He then went on to earn an MSc (1974) and a PhD (1978) from the University of the West Indies at St. Augustine in geology, specializing in geochemistry . [ 12 ] [ 13 ] At the university, as researcher, he held the positions of research fellow and later as head of the Seismic Research Unit . Rowley was general manager of state-owned National Quarries Company Limited as well. [ 10 ]
Rowley entered politics in 1981, where he unsuccessfully contested the Tobago West seat in the general election of that year. To date he has the distinction of being the only People's National Movement candidate to have contested a seat in a General Election in both Tobago and Trinidad. He first served in Parliament as an Opposition Senator from 1987 to 1990 (3rd Parliament). Subsequently, he was appointed as Minister of Agriculture, Land and Marine Resources (4th Parliament), Minister of Planning and Development and Minister of Housing (as cabinet reshuffled) (8th Parliament) and Minister of Trade and Industry (9th Parliament) until he was fired by then Prime Minister Patrick Manning .
Following the People's National Movement 's defeat in the 2010 general election , Rowley was appointed as Leader of the Opposition on the 1st June. [ 14 ] He was then elected political leader of the People's National Movement as he was seen as the most capable to lead the party. As political leader he advocated implementation of the one man, one vote system within the party. Rowley has served on several parliamentary committees. In 2004, he chaired the Joint Select Committee of Parliament which examined and made recommendations for the live broadcasting of parliamentary debates. He served as the representative governor of Trinidad and Tobago for the Inter-American Development Bank and the Caribbean Development Bank . [ 9 ]
Rowley led the People's National Movement in the September 2015 general election , in which his party secured 23 out of 41 seats in the House of Representatives to form the government, defeating the previous People's Partnership coalition government. On 9 September 2015, Rowley was sworn in as Prime Minister of Trinidad and Tobago by President Anthony Carmona . [ 15 ] He becomes the seventh Prime Minister of Trinidad and Tobago and the second Tobago-born Prime Minister. Rowley again led the People's National Movement to victory in the 2020 Trinidad and Tobago general election for a second term in government under his premiership. He was sworn in as Prime Minister of Trinidad and Tobago on 19 August by President Paula-Mae Weekes at the President's House in St. Anns after the opposition party asked for recounts to be done in marginal constituencies. [ 16 ]
During his tenure, on 5 February 2022, the Trinidad and Tobago coast guard fired upon a vessel with Venezuelan migrants while attempting to stop it, killing a nine-month-old baby and injuring his mother. The coast guard claimed that the shots were fired "in self-defense". [ 17 ] Rowley deemed the action "legal and appropriate"; the Trinidadian police and coast guard opened an investigation of the event. [ 18 ]
At the PNM convention in August 2024, Rowley announced his support for the Caribbean Court of Justice to replace the Judicial Committee of the Privy Council as Trinidad and Tobago's final court of appeals. He also announced his government would legislate to remove Christopher Columbus 's ships from the national coat of arms and replace them with the steelpan drum, which had been declared the official national music instrument a few months earlier. He stated that the changes would "signal that we are on our way to removing the colonial vestiges that we have in our country". [ 19 ]
He appointed the following people as his cabinet:
He is married to attorney-at-law Sharon Rowley and has three children, [ 9 ] and is a member of the Seventh-day Adventist Church . [ 21 ] | https://en.wikipedia.org/wiki/Keith_Rowley |
Kekulé was a computer program named after the chemist Friedrich August Kekulé von Stradonitz . The program was created starting in about 1990 by Joe McDaniel and Jason Balmuth while at Fein-Marquart Associates with funding from the National Cancer Institute under a Small Business Innovative Research Grant .
The program was created to satisfy a need at the NCI for entering chemical structures into a database . The format required for the database was a connection table while the published form of a structure was a drawing. The program could take a scanned image of the drawn structure and automatically read the atom labels (characters) and lines between atoms (bonds) to create the connection table for input into the database.
NCI has ceased to use the program. [ 1 ]
Several articles describing the internal operation of the program were written and published in refereed journals such as the Journal of Chemical Information and Computer Sciences . [ 2 ]
This article about chemistry software is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Kekulé_Program |
In non-equilibrium physics , the Keldysh formalism or Keldysh–Schwinger formalism is a general framework for describing the quantum mechanical evolution of a system in a non-equilibrium state or systems subject to time varying external fields ( electrical field , magnetic field etc.). Historically, it was foreshadowed by the work of Julian Schwinger and proposed almost simultaneously by Leonid Keldysh [ 1 ] and, separately, Leo Kadanoff and Gordon Baym . [ 2 ] It was further developed by later contributors such as O. V. Konstantinov and V. I. Perel . [ 3 ]
Extensions to driven-dissipative open quantum systems is given not only for bosonic systems, [ 4 ] but also for fermionic systems. [ 5 ]
The Keldysh formalism provides a systematic way to study non-equilibrium systems, usually based on the two-point functions corresponding to excitations in the system. The main mathematical object in the Keldysh formalism is the non-equilibrium Green's function (NEGF), which is a two-point function of particle fields. In this way, it resembles the Matsubara formalism , which is based on equilibrium Green functions in imaginary-time and treats only equilibrium systems.
Consider a general quantum mechanical system. This system has the Hamiltonian H 0 {\displaystyle H_{0}} . Let the initial state of the system be the pure state | n ⟩ {\displaystyle |n\rangle } . If we now add a time-dependent perturbation to this Hamiltonian, say H ′ ( t ) {\displaystyle H'(t)} , the full Hamiltonian is H ( t ) = H 0 + H ′ ( t ) {\displaystyle H(t)=H_{0}+H'(t)} and hence the system will evolve in time under the full Hamiltonian. In this section, we will see how time evolution actually works in quantum mechanics.
Consider a Hermitian operator O {\displaystyle {\mathcal {O}}} . In the Heisenberg picture of quantum mechanics, this operator is time-dependent and the state is not. The expectation value of the operator O ( t ) {\displaystyle {\mathcal {O}}(t)} is given by
where, due to time evolution of operators in the Heisenberg picture, O ( t ) = U † ( t , 0 ) O ( 0 ) U ( t , 0 ) {\displaystyle {\mathcal {O}}(t)=U^{\dagger }(t,0){\mathcal {O}}(0)U(t,0)} . The time-evolution unitary operator U ( t 2 , t 1 ) {\displaystyle U(t_{2},t_{1})} is the time-ordered exponential of an integral, U ( t 2 , t 1 ) = T ( e − i ∫ t 1 t 2 H ( t ′ ) d t ′ ) . {\displaystyle U(t_{2},t_{1})=T(e^{-i\int _{t_{1}}^{t_{2}}H(t')dt'}).} (Note that if the Hamiltonian at one time commutes with the Hamiltonian at different times, then this can be simplified to U ( t 2 , t 1 ) = e − i ∫ t 1 t 2 H ( t ′ ) d t ′ {\displaystyle U(t_{2},t_{1})=e^{-i\int _{t_{1}}^{t_{2}}H(t')dt'}} .)
For perturbative quantum mechanics and quantum field theory , it is often more convenient to use the interaction picture . The interaction picture operator is
where U 0 ( t 1 , t 2 ) = e − i H 0 ( t 1 − t 2 ) {\displaystyle U_{0}(t_{1},t_{2})=e^{-iH_{0}(t_{1}-t_{2})}} . Then, defining S ( t 1 , t 2 ) = U 0 † ( t 1 , t 2 ) U ( t 1 , t 2 ) , {\displaystyle S(t_{1},t_{2})=U_{0}^{\dagger }(t_{1},t_{2})U(t_{1},t_{2}),} we have
Since the time-evolution unitary operators satisfy U ( t 3 , t 2 ) U ( t 2 , t 1 ) = U ( t 3 , t 1 ) {\displaystyle U(t_{3},t_{2})U(t_{2},t_{1})=U(t_{3},t_{1})} , the above expression can be rewritten as
or with ∞ {\displaystyle \infty } replaced by any time value greater than t {\displaystyle t} .
We can write the above expression more succinctly by, purely formally, replacing each operator X ( t ) {\displaystyle X(t)} with a contour-ordered operator X ( c ) {\displaystyle X(c)} , such that c {\displaystyle c} parametrizes the contour path on the time axis starting at t = 0 {\displaystyle t=0} , proceeding to t = ∞ {\displaystyle t=\infty } , and then returning to t = 0 {\displaystyle t=0} . This path is known as the Keldysh contour. X ( c ) {\displaystyle X(c)} has the same operator action as X ( t ) {\displaystyle X(t)} (where t {\displaystyle t} is the time value corresponding to c {\displaystyle c} ) but also has the additional information of c {\displaystyle c} (that is, strictly speaking X ( c 1 ) ≠ X ( c 2 ) {\displaystyle X(c_{1})\neq X(c_{2})} if c 1 ≠ c 2 {\displaystyle c_{1}\neq c_{2}} , even if for the corresponding times X ( t 1 ) = X ( t 2 ) {\displaystyle X(t_{1})=X(t_{2})} ).
Then we can introduce notation of path ordering on this contour, by defining T c ( X ( 1 ) ( c 1 ) X ( 2 ) ( c 2 ) … X ( n ) ( c n ) ) = ( ± 1 ) σ X ( σ ( 1 ) ) ( c σ ( 1 ) ) X ( σ ( 2 ) ) ( c σ ( 2 ) ) … X ( σ ( n ) ) ( c σ ( n ) ) {\displaystyle {\mathcal {T_{c}}}(X^{(1)}(c_{1})X^{(2)}(c_{2})\ldots X^{(n)}(c_{n}))=(\pm 1)^{\sigma }X^{(\sigma (1))}(c_{\sigma (1)})X^{(\sigma (2))}(c_{\sigma (2)})\ldots X^{(\sigma (n))}(c_{\sigma (n)})} , where σ {\displaystyle \sigma } is a permutation such that c σ ( 1 ) < c σ ( 2 ) < … c σ ( n ) {\displaystyle c_{\sigma (1)}<c_{\sigma (2)}<\ldots c_{\sigma (n)}} , and the plus and minus signs are for bosonic and fermionic operators respectively. Note that this is a generalization of time ordering .
With this notation, the above time evolution is written as
Where c {\displaystyle c} corresponds to the time t {\displaystyle t} on the forward branch of the Keldysh contour, and the integral over c ′ {\displaystyle c'} goes over the entire Keldysh contour. For the rest of this article, as is conventional, we will usually simply use the notation X ( t ) {\displaystyle X(t)} for X ( c ) {\displaystyle X(c)} where t {\displaystyle t} is the time corresponding to c {\displaystyle c} , and whether c {\displaystyle c} is on the forward or reverse branch is inferred from context.
The non-equilibrium Green's function is defined as i G ( x 1 , t 1 , x 2 , t 2 ) = ⟨ n | T ψ ( x 1 , t 1 ) ψ ( x 2 , t 2 ) | n ⟩ {\displaystyle {\begin{aligned}iG(x_{1},t_{1},x_{2},t_{2})=\langle n|T\psi (x_{1},t_{1})\psi (x_{2},t_{2})|n\rangle \end{aligned}}} .
Or, in the interaction picture, i G ( x 1 , t 1 , x 2 , t 2 ) = ⟨ n | T c ( e − i ∫ c H ′ ( t ′ ) d t ′ ψ ( x 1 , t 1 ) ψ ( x 2 , t 2 ) ) | n ⟩ {\displaystyle {\begin{aligned}iG(x_{1},t_{1},x_{2},t_{2})=\langle n|{\mathcal {T_{c}}}(e^{-i\int _{c}H'(t')dt'}\psi (x_{1},t_{1})\psi (x_{2},t_{2}))|n\rangle \end{aligned}}} . We can expand the exponential as a Taylor series to obtain the perturbation series
This is the same procedure as in equilibrium diagrammatic perturbation theory, but with the important difference that both forward and reverse contour branches are included.
If, as is often the case, H ′ {\displaystyle H'} is a polynomial or series as a function of the elementary fields ψ {\displaystyle \psi } , we can organize this perturbation series into monomial terms and apply all possible Wick pairings to the fields in each monomial, obtaining a summation of Feynman diagrams . However, the edges of the Feynman diagram correspond to different propagators depending on whether the paired operators come from the forward or reverse branches. Namely,
where the anti-time ordering T ¯ {\displaystyle {\mathcal {\overline {T}}}} orders operators in the opposite way as time ordering and the ± {\displaystyle \pm } sign in G 0 − + {\displaystyle G_{0}^{-+}} is for bosonic or fermionic fields. Note that G 0 − − {\displaystyle G_{0}^{--}} is the propagator used in ordinary ground state theory.
Thus, Feynman diagrams for correlation functions can be drawn and their values computed the same way as in ground state theory, except with the following modifications to the Feynman rules: Each internal vertex of the diagram is labeled with either + {\displaystyle +} or − {\displaystyle -} , while external vertices are labelled with − {\displaystyle -} . Then each (unrenormalized) edge directed from a vertex a {\displaystyle a} (with position x a {\displaystyle x_{a}} , time t a {\displaystyle t_{a}} and sign s a {\displaystyle s_{a}} ) to a vertex b {\displaystyle b} (with position x b {\displaystyle x_{b}} , time t b {\displaystyle t_{b}} and sign s b {\displaystyle s_{b}} ) corresponds to the propagator G 0 s a s b ( x a , t a , x b , t b ) {\displaystyle G_{0}^{s_{a}s_{b}}(x_{a},t_{a},x_{b},t_{b})} . Then the diagram values for each choice of ± {\displaystyle \pm } signs (there are 2 v {\displaystyle 2^{v}} such choices, where v {\displaystyle v} is the number of internal vertices) are all added up to find the total value of the diagram. | https://en.wikipedia.org/wiki/Keldysh_formalism |
In metallurgy , Keller's reagent is a mixture of nitric acid , hydrochloric acid , and hydrofluoric acid , used to etch aluminum alloys to reveal their grain boundaries and orientations. [ 1 ] It is also sometimes called Dix–Keller reagent , after E. H. Dix, Jr., and Fred Keller of the Aluminum Corporation of America , who pioneered the use of this technique in the late 1920s and early 1930s. [ 2 ] [ 3 ]
Keller's reagent contains oxidizing nitric acid and toxic hydrofluoric acid. The reagent and its fumes may be lethal via contact, inhalation of its fumes, etc. Hydrogen produced on contact with some metals may pose a fire hazard. [ 4 ]
This metalworking article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Keller's_reagent_(metallurgy) |
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