## magnification – MFD equals 4x focal length? But published specs contradict that

I spent the better part of this evening perusing the series of equations behind this popular magnification calculator.

Equation F10 states `d ≥ 4f`, where `d` is focus distance and `f` is focal length. I followed the math up to here, and it makes sense to me. I did some testing with one of my all-around lenses, and the results fit within these equations. All of this suggests that MFD is 4x a lens’ focal length.

So how then can the Sony FE 90mm F2.8 macro lens have `d = 280mm` and `f = 90mm`? This would appear to violate the previously defined limit, since 280 < 4*90. What am I missing?

EDIT: I found the concept of “focus breathing” and added it below as an answer. But, I have a followup question. Does this mean after the focus breathing, the 90mm truly is focused at a focal length of 70mm? (i.e. 280mm/4) This seems like a non-trivial change; whereas the definition of focus breathing describes these changes as “small”.

## java – An attempt is made to write an equals method on a class that contains an array of objects

I am trying to write a college class method that compares the contents of the arrays of the two objects in the college class. So the method compares the Student () array in the college object with the other Student () array in another college object and the same for the Teacher () array. I wrote an equivalent method for this, but it looks too long and not pretty. What better way to write it?

College class

``````public class College
{
private Student() student;
private Teacher() teacher;
public College()
{
student = new Student(9);
teacher = new Teacher(9);
}

public Student() getStudent()
{
return student;
}

public void setStudent(Student() student)
{
this.student = student;
}

public Teacher() getTeacher()
{
return teacher;
}

public void setTeacher(Teacher() teacher)
{
this.teacher = teacher;
}

**public boolean equals(Object inObj)
{// this equals method

boolean isEqual = false;
College inCollege = (College)inObj;

if(student.length == inCollege.getStudent().length)
{
for(int i = 0; i < student.length; i++)
{
if(student(i).equals(inCollege.student(i)))
{
isEqual = true;
}
}
}
if((teacher.length == inCollege.getTeacher().length) && isEqual == true)
{
isEqual = false;
for(int i = 0; i < inCollege.getTeacher().length; i++ )
{
if(teacher(i).equals(inCollege.teacher(i)))
{ System.out.println("im in");
isEqual = true;
}
}
}
return isEqual;
}**
}
``````

Student class

``````public class Student
{
private String name;
private int age;

public Student()
{
name = "Samrah";
age = 19;
}

public Student(String name, int age)
{
this.name = name;
this.age = age;
}
public String getName()
{
return name;
}

public void setName(String name)
{
this.name = name;
}

public int getAge()
{
return age;
}

public void setAge(int age)
{
this.age = age;
}

public boolean equals(Object inObj)
{
boolean isEqual = false;
if(inObj instanceof Student)
{
Student inStudent = (Student)inObj;
if(this.name.equals(inStudent.getName()))
if(this.age == inStudent.getAge())
isEqual = true;

}
return isEqual;
}

public String toString()
{
String str;

return str = "name: "+name+" age: "+age;
}

}
``````

Teacher class

``````public class Teacher
{
private String name;
private int age;

public Teacher()
{
name = "Sanjay";
age = 45;
}

public Teacher(String name, int age)
{
this.name = name;
this.age = age;
}

public void setName(String name)
{
this.name = name;
}

public String getName()
{
return name;
}

public int getAge()
{
return age;
}

public void setAge(int age)
{
this.age = age;
}

public boolean equals(Object inObj)
{
boolean isEqual = false;
if(inObj instanceof Teacher)
{
Teacher inTeacher = (Teacher)inObj;
if(this.name.equals(inTeacher.getName()))
if(this.age == inTeacher.getAge())
isEqual = true;

}
return isEqual;
}

public String toString()
{
String str;

return str = "name: "+name+" age: "+age;
}
}
``````

Trying to do something like this:

``````    boolean isEqual = false;

if(inObject instanceof EngineClass)
{
EngineClass inEngine = (EngineClass)inObject;
if(cylinders == inEngine.getCylinders())
if(fuel.equals(inEngine.getFuel()))
isEqual = true;
}
return isEqual;
``````

But since it's an array, I have to go through the arrays so I'm really confused.

## Java – Is it a good idea to have logic in the Equals method that doesn't do an exact match?

While assisting a student on a university project, we were working on a university-provided Java exercise that defined a class for an address with the following fields:

``````number
street
city
zipcode
``````

And it was determined that the equality logic should return true if the number and the zip code match.

I was once taught that the Equals method should only make an exact comparison between the objects (after checking the pointer), which makes sense to me, but contradicts the task given to them.

I can see why you want to override the logic so you can use things like `list.contains()` with your partial agreement, but I wonder if this is considered kosher, and if not why not?

## Real Analysis – Suppose \$ F \$ is a limited variation. How can we show that the total variation is the integral of \$ | F & # 39; | \$ equals if \$ F \$ is absolutely continuous?

The problem stems from Stein's Real Analysis Exercise 16 in Chapter 3: Let's assume the function $$F (x)$$ is of limited variation $$(a, b)$$, To let $$T_F (a, b)$$ denote the total variation of $$F$$ on $$(a, b)$$, Then $$F (x)$$ is switched on absolutely continuously $$(a, b)$$ then and only if $$int_a ^ b | F & # 39; (x) | mathrm {d} x = T_F (a, b).$$
I tried very hard, but I cannot point out the absolute continuity from the above equation.
Any help is appreciated.

## sql server – Retrieves the CreatedAt timestamp when the number of rows equals a specified number

You could try it

``````SELECT
id
, createdAt
FROM (
SELECT
id
, createdAt
, RANK() OVER (PARTITION BY OtherId ORDER BY createdAt) rnk
FROM Table1
) AS S
WHERE rnk = 8
;
``````

The inner `SELECT` groups the records after OtherId, orders and orders them made in, The outer one `SELECT` selects the record after a specific number.

The mentioned CTE (Common Table Expression) @Akina would pull up the subselection:

``````WITH
S (id, createdAt, rnk) AS (
SELECT
id
, createdAt
, RANK() OVER (PARTITION BY OtherId ORDER BY createdAt) rnk
FROM Table1
)
SELECT
id
, createdAt
FROM S
WHERE rnk = 8
;
``````

Do not see much difference in this case. However, the technique helps a lot with more complex settings because it allows you to extend the instructions and is usually easier to read.

See it in action: db <> violin

Please comment if and how this requires customization / further details.

## Reference Request – \$ n \$ is a positive prime if \$ k ^ {n-1} 1 \$ mod \$ n \$ equals \$ 1

When I read the little sentence from Fermat, I found a problem. After that, I realized that the problem is the Chinese Hypothesis.

When I read Wilson's sentence, I found that $$(p-2)! equiv -1$$ mod $$p$$ but after that I knew that this is a special case of the Sylow sentences.

I can not prove, can not verify by my computer the following statement, because the Chinese hypothesis is up to true $$n = {340}$$ With $$k$$ is constant $$2$$, Here I leave $$1

Is it true that if $$n$$ is a positive prime, if only if $$k ^ {n-1} equiv 1$$ mod $$n$$ With $$1

• If $$n$$ is a positive prime after the small Fermat theorem $$Rightarrow$$ $$k ^ {n-1} equiv 1$$ mod $$n$$,

• If $$k ^ {n-1} equiv 1$$ mod $$n$$ With $$k = 1, 2, 3, …, n-1$$ then $$n$$ is also prime.

## nt.number theory – For a problem where \$ frac { text {prime} -1} { operatorname {rad} ( text {prime} -1)} \$ equals the sequence of primors

We denote whole numbers $$m> 1$$ share the product of different primes $$m$$ as $$operatorname {rad} (m) = prod_ { substack {p mid m \ p text {prime}}} p,$$
with the definition $$operatorname {rad} (1) = 1$$ (see you want the Wikipedia Radical of an integer), this is the famous multiplicative function in the statement of the abc conjecture. We also call that $$k$$th primorial as $$N_k = prod_ {t = 1} ^ k p_t$$ this is the product of the first $$k$$ Primes.

I was inspired in the first paragraph of the section B46 (1) to propose a variant of the type of problem the book presents. I think about solutions $$(p, k)$$, from where $$p$$ always denotes a prime number for which the identity
$$frac {p-1} { operatorname {rad} (p-1)} = N_k tag {1}$$
applies to some primitive ones $$N_k$$With $$k geq 1$$,

I've used a Pari / GP program to write the first satisfying primes $$(1)$$, these first few primes $$p$$are (this is a selection of my calculations) $$5,13,29,37,53,61,149,157,173,181,229, 269,277,$$ $$293,317, ldots$$ which correspond to these indices $$k$$& # 39; s
$$1,1,1,2,1,1,1,1,1,2,1,1,1,1 ldots$$ our origins $$N_k$$ fulfill the equation $$(1)$$,

The curiosity that I have is something about the size or cardinality of the set $$mathcal {K} = {k geq 1: (p, k) text {is a solution to the equation} (1) }.$$

Guess. The sentence $$mathcal {K}$$ is finally,

So what I'm saying is the set $$mathcal {K}$$ remains as a finite / finite set of positive integers, if the other variable $$p$$ Runs over the set of all primes.

Question. Can one refute earlier assumptions? Can you do some thinking or calculations
clarify the truthfulness of the conjecture? Many thanks.

Maybe they can be useful state boundaries or an approximation to cardinality $$| mathcal {K} |$$ for increasing segments of primes $$2 leq p leq X$$ and primors with indices $$1 leq k leq Y$$

Under these circumstances, I have no idea whether previous guesses are true, but I said I just want to find solutions to the integers $$k = 1.2$$ and $$3$$ (I do not know if my contribution to this sequence has good mathematical content, the comments are welcome).

## references:

(1) Richard K. Guy, Unresolved Problems in Number Theory, Unresolved Problems in Intuitive Mathematics Volume I, 2nd Edition, Springer-Verlag (1994).

## Hetzner is incredible. Are there equals?

I like Hetzner very, very cheap for what you get. I know it's old hardware, but with 2 servers all have been knocking on wood so far. If you run it as a RAID, you can feel more secure.

Let's say I have an Intel Core i7-3770 with 2 x 3TB hard drive and 16GB of RAM for \$ 25 a month. This includes unlimited traffic on 1 Gbps uplink. Config is almost perfect and all I can wish for is a stronger CPU.

So look for something like that. Powerful machine, no SSD, 2-3 TB x 2 HDD and 1 Gbps with at least 100 TB of data traffic, unmeasured or unlimited is best

I've done some homework, reviewed the last 2 pages of offers and found nothing … Please specify where to look. Oh yes, I just want to diversify my eggs and divide between different geos / providers.

## Given a value that I need to know until the number equals a list of numbers and their index

I have a list of ascending order of numbers. For a given value, I have to know until the number matches the array and its index.

``````list myLista = new list(New[] {"2", "9", "17", "25", "35", "42", "70"});
``````

Initial index = 0.
At a value of 5, the index would be 1 and the number 9
At a value of 17, the index would be 2 and the number 17
For a value = 0, the index would be 0 and the number 2

## Hessian matrix equals zero

The function $$x times y + e ^ {- x times y}$$ if the points that make up the x-axis and the y-axis are critical points, how can I prove that they are points with a minimum, then the Hessian matrix is ​​zero at these points.